ꯔꯨꯂꯦꯠ ꯕꯦꯠ ꯊꯝꯕꯒꯤ ꯊꯧꯔꯥꯡꯁꯤꯡ · ꯅꯦꯒꯦꯇꯤꯕ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯟ · ꯃꯤꯅꯤꯠ 8

ꯐꯤꯕꯣꯅꯥꯆꯤ ꯔꯨꯂꯦꯠ ꯊꯧꯔꯥꯡ

ꯐꯤꯕꯣꯅꯥꯆꯤ ꯔꯨꯂꯦꯠ ꯊꯧꯔꯥꯡꯗ ꯊꯝꯂꯕ ꯁꯦꯜꯁꯤꯡꯅ 1, 1, 2, 3, 5, 8, 13… ꯃꯇꯨꯡ ꯏꯟꯅꯩ꯫ ꯃꯥꯏꯊꯤꯕꯒꯤ ꯃꯇꯨꯡꯗ ꯈꯣꯡꯊꯥꯡ ꯑꯃꯥ ꯃꯃꯥꯡꯗ ꯆꯠꯂꯤ, ꯃꯥꯏꯄꯥꯛꯄꯒꯤ ꯃꯇꯨꯡꯗ ꯈꯣꯡꯊꯥꯡ ꯑꯅꯤ ꯍꯟꯊꯔꯛꯂꯤ꯫

ꯊꯨꯅ ꯄꯥꯎꯈꯨꯝ

ꯃꯁꯤꯅ ꯆꯛꯔꯕꯨ ꯃꯥꯏꯊꯤꯍꯟꯗꯦ; ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ ꯊꯧꯔꯥꯡ ꯑꯃꯠꯇꯅ ꯉꯝꯗꯦ꯫ ꯃꯁꯤ ꯃꯥꯔꯇꯤꯟꯒꯦꯜꯗꯒꯤ ꯍꯦꯟꯅꯥ ꯇꯞꯄ ꯑꯣꯏ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯉꯝꯈꯩꯗ ꯌꯧꯗ꯭ꯔꯤꯉꯩꯗ ꯍꯦꯟꯅꯥ ꯁꯥꯡꯕ ꯃꯥꯏꯊꯤꯕꯒꯤ ꯁ꯭ꯇ꯭ꯔꯤꯛꯁꯤꯡ ꯂꯥꯟꯊꯣꯀꯏ, ꯑꯃꯁꯨꯡ ꯍꯦꯟꯅꯥ ꯇꯞꯅ ꯑꯃꯨꯛ ꯍꯟꯅꯥ ꯐꯪꯏ꯫ ꯃꯥꯡꯒꯗꯕ ꯁꯦꯜ ꯑꯁꯤ ꯇꯔꯅꯑꯣꯚꯔꯒꯤꯁꯦꯜꯇꯔꯅꯑꯣꯚꯔꯁꯦꯁꯟ ꯅꯠꯔꯒ ꯃꯇꯝ ꯑꯃꯒꯤ ꯃꯅꯨꯡꯗ ꯕꯦꯠ ꯊꯝꯂꯕ ꯁꯦꯜ ꯄꯨꯝꯅꯃꯛ, ꯑꯃꯨꯛ ꯍꯟꯅꯥ ꯊꯝꯂꯕ ꯃꯥꯏꯄꯥꯛꯇꯨꯅ ꯐꯪꯂꯕ ꯁꯦꯜꯁꯨ ꯌꯥꯎꯅ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯍꯦꯟꯗꯜ, ꯑꯦꯛꯁꯟ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → 2.70% ꯑꯗꯨꯃꯛꯅꯤ꯫

ꯁꯤꯛꯋꯦꯟꯁ

1 1 2 3 5 8 13 21

ꯃꯥꯏꯊꯤꯕꯒꯤ ꯃꯇꯨꯡꯗ

+1 ꯈꯣꯡꯊꯥꯡ

ꯃꯥꯏꯄꯥꯛꯄꯒꯤ ꯃꯇꯨꯡꯗ

−2 ꯈꯣꯡꯊꯥꯡ

$10 ꯗꯒꯤ ꯍꯧꯔꯒ ꯉꯝꯈꯩ $500

ꯃꯥꯏꯊꯤꯕ ~10 ꯒꯤ ꯃꯇꯨꯡꯗ

ꯁꯤꯛꯋꯦꯟꯁ ꯑꯁꯤ ꯀꯔꯝꯅ ꯁꯦꯝꯕꯒꯦ

ꯃꯁꯤꯡ ꯈꯨꯗꯤꯡꯃꯛ ꯃꯃꯥꯡꯗ ꯂꯩꯕ ꯃꯁꯤꯡ ꯑꯅꯤꯒꯤ ꯄꯨꯟꯁꯤꯟꯕꯅꯤ꯫

ꯃꯔꯝ ꯑꯗꯨꯅ 8 ꯑꯃꯁꯨꯡ 13ꯒꯤ ꯃꯇꯨꯡꯗ 21 ꯂꯥꯛꯏ꯫

ꯃꯁꯤꯡ ꯈꯨꯗꯤꯡꯃꯛ ꯁ꯭ꯀ꯭ꯋꯥꯌꯔ ꯑꯃꯥ ꯑꯣꯏꯅ ꯌꯦꯛꯂꯕꯗ ꯁ꯭ꯀ꯭ꯋꯥꯌꯔꯁꯤꯡ ꯑꯗꯨ ꯆꯨꯅ ꯆꯥꯟꯅꯩ: ꯑꯅꯧꯕ ꯈꯨꯗꯤꯡꯃꯛꯀꯤ ꯁꯥꯡꯕ ꯑꯁꯤ ꯃꯃꯥꯡꯒꯤ ꯑꯅꯤ ꯑꯗꯨ ꯃꯅꯥꯛ ꯃꯅꯥꯛꯇ ꯊꯃꯂꯕꯒꯤ ꯁꯥꯡꯕꯒ ꯃꯥꯟꯅꯩ꯫ ꯁ꯭ꯀ꯭ꯋꯥꯌꯔ ꯈꯨꯗꯤꯡꯃꯛꯇ ꯀꯣꯏꯅꯒꯤ ꯃꯔꯤꯁꯨꯕ ꯁꯔꯨꯛ ꯑꯃꯥ ꯌꯦꯛꯂꯕꯗ ꯃꯈꯣꯌ ꯄꯨꯟꯅꯗꯨꯅ ꯁ꯭ꯄꯥꯏꯔꯦꯜ ꯑꯃꯥ ꯑꯣꯏꯔꯛꯏ꯫

ꯁꯤꯛꯋꯦꯟꯁ ꯑꯗꯨꯗ ꯆꯠꯄ

ꯃꯥꯏꯊꯤꯕ ꯑꯃꯅ ꯈꯣꯡꯊꯥꯡ ꯑꯃꯥ ꯃꯃꯥꯡꯗ ꯆꯠꯍꯜꯂꯤ꯫ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯃꯅ ꯈꯣꯡꯊꯥꯡ ꯑꯅꯤ ꯃꯇꯨꯡꯗ ꯍꯜꯂꯛꯍꯜꯂꯤ꯫

ꯃꯊꯪꯒꯤ ꯊꯝꯂꯕ ꯁꯦꯜ1ꯍꯧꯖꯤꯛ ꯐꯥꯑꯣꯕꯒꯤ ꯃꯍꯩ0ꯁ꯭ꯄꯤꯟ0

ꯊꯝꯂꯕ ꯁꯦꯜ ꯑꯃꯁꯨꯡ ꯃꯍꯩꯁꯤꯡ ꯑꯁꯤ ꯍꯧꯔꯛꯐꯃꯒꯤ ꯕꯦꯠꯀꯤ ꯌꯨꯅꯤꯠꯇꯅꯤ꯫

ꯐꯤꯕꯣꯅꯥꯆꯤ ꯔꯨꯂꯦꯠ ꯁꯤꯁ꯭ꯇꯦꯝꯅ ꯀꯔꯝꯅ ꯊꯕꯛ ꯇꯧꯕꯒꯦ?

ꯐꯤꯕꯣꯅꯥꯆꯤꯊꯧꯔꯥꯡꯐꯤꯕꯣꯅꯥꯆꯤ1, 1, 2, 3, 5, 8, 13… ꯁꯤꯛꯋꯦꯟꯁ ꯃꯇꯨꯡ ꯏꯟꯕ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯟ: ꯃꯥꯏꯊꯤꯔꯕꯥ ꯃꯇꯨꯡꯗ ꯈꯣꯡꯊꯥꯡ ꯑꯃꯥ ꯃꯃꯥꯡꯗ, ꯃꯥꯏꯄꯥꯛꯂꯕꯥ ꯃꯇꯨꯡꯗ ꯈꯣꯡꯊꯥꯡ ꯑꯅꯤ ꯃꯇꯨꯡꯗ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯃꯁꯤꯡꯁꯤꯡ ꯏꯕꯤꯌꯨ: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144꯫ ꯃꯁꯤꯡ ꯈꯨꯗꯤꯡꯃꯛ ꯃꯃꯥꯡꯒꯤ ꯃꯁꯤꯡ ꯑꯅꯤꯒꯤ ꯃꯄꯨꯡꯅꯤ꯫ ꯑꯍꯥꯅꯕꯗꯒꯤ ꯍꯧꯗꯨꯅ ꯃꯗꯨꯒꯤ ꯃꯁꯤꯡꯒꯤ ꯌꯨꯅꯤꯠꯁꯦꯜꯌꯨꯅꯤꯠꯁꯤꯁ꯭ꯇꯦꯝ ꯅꯠꯔꯒ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯅ ꯁꯤꯖꯤꯟꯅꯕ ꯃꯔꯨꯑꯣꯏꯕ ꯊꯝꯂꯕ ꯁꯦꯜ꯫ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯅꯁꯤꯡ ꯌꯨꯅꯤꯠꯇ ꯁꯟꯗꯣꯛꯂꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯈꯣꯌ ꯀꯔꯤꯒꯨꯝꯕ ꯇꯦꯕꯜꯗ ꯆꯠꯂꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯊꯝꯕꯤꯌꯨ꯫ ꯃꯥꯏꯊꯤꯔꯕꯗ ꯈꯣꯡꯊꯥꯡ ꯑꯃꯥ ꯌꯦꯠꯊꯪꯗ ꯆꯠꯂꯣ꯫ ꯃꯥꯏꯄꯥꯛꯂꯕꯗ ꯈꯣꯡꯊꯥꯡ ꯑꯅꯤ ꯑꯣꯏꯊꯪꯗ ꯆꯠꯂꯣ, ꯃꯐꯝ ꯂꯩꯇ꯭ꯔꯕꯗ ꯍꯧꯔꯀꯐꯃꯗ ꯍꯜꯂꯛꯂꯣ꯫ ꯁꯤꯁ꯭ꯇꯦꯝ ꯄꯨꯝꯅꯃꯛ ꯃꯁꯤꯅꯤ꯫ ꯇꯦꯕꯜꯅ ꯈꯣꯡꯊꯥꯡ ꯈꯨꯗꯤꯡꯃꯛ ꯀꯌꯥ ꯌꯥꯎꯕꯒꯦ ꯎꯠꯂꯤ: ꯇꯦꯕꯜꯒꯤ ꯉꯝꯈꯩꯇꯦꯕꯜꯇꯦꯕꯜꯒꯤ ꯉꯝꯈꯩꯌꯥꯍꯜꯂꯤꯕ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯅꯦꯝꯕ ꯑꯃꯁꯨꯡ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯋꯥꯡꯕ ꯕꯦꯠ꯫ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯋꯥꯡꯕ ꯉꯝꯈꯩ ꯑꯗꯨꯅ ꯑꯅꯤ ꯊꯥꯛ ꯍꯦꯅꯒꯠꯍꯟꯕ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯅꯁꯤꯡ ꯊꯤꯡꯏ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯅꯠꯔꯒ ꯅꯍꯥꯛꯀꯤ ꯕꯦꯡꯀꯔꯣꯜꯅꯁꯦꯜꯕꯦꯡꯀꯔꯣꯜꯁꯥꯟꯅꯅꯕ ꯇꯣꯉꯥꯟꯅ ꯊꯝꯂꯕ ꯁꯦꯜ ꯄꯨꯝꯅꯃꯛ꯫ ꯕꯦꯡꯀꯔꯣꯜ ꯃꯦꯅꯦꯖꯃꯦꯟꯠ ꯍꯥꯌꯕꯁꯤ ꯃꯗꯨꯒꯤ ꯀꯌꯥ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯗ ꯑꯃꯁꯨꯡ ꯁꯦꯁꯟ ꯈꯨꯗꯤꯡꯗ ꯈꯨꯗꯣꯡꯊꯤꯕꯗ ꯊꯃꯒꯗꯒꯦ ꯍꯥꯌꯕ ꯋꯥꯔꯦꯞ ꯂꯧꯕꯅꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯊꯤꯡꯖꯤꯜꯂꯕ ꯃꯥꯏꯊꯤꯕꯒꯤ ꯁ꯭ꯇ꯭ꯔꯤꯛ ꯑꯃꯅ ꯃꯇꯝ ꯑꯗꯨ ꯐꯥꯑꯣꯕ ꯊꯃꯈꯤꯕ ꯄꯨꯝꯅꯃꯛꯀꯤ ꯃꯄꯨꯡ ꯃꯥꯡꯍꯜꯂꯤ꯫

ꯈꯣꯡꯊꯥꯡꯊꯝꯂꯕ ꯁꯦꯜ (ꯌꯨꯅꯤꯠ)ꯄꯨꯟꯁꯤꯜꯂꯕ ꯈꯨꯗꯣꯡꯊꯤꯕꯃꯥꯏꯄꯥꯛꯄꯒꯤ ꯃꯇꯨꯡꯗ ꯅꯦꯠ

111+1

2120

3240

437−1

5512−2

6820−4

71333−7

82154−12

93488−20

1055143−33

1189232−54

12144376−88

ꯄꯨꯟꯁꯤꯜꯂꯕ ꯈꯨꯗꯣꯡꯊꯤꯕ ꯍꯥꯌꯕꯁꯤ ꯁꯤꯛꯋꯦꯟꯁ ꯑꯗꯨꯒꯤ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯃꯛ ꯃꯥꯏꯊꯤꯔꯕꯗ ꯃꯥꯡꯒꯗꯕ ꯄꯨꯝꯅꯃꯛꯅꯤ꯫ ꯌꯨꯅꯤꯠ ꯑꯃꯗ $10 ꯑꯣꯏꯔꯕꯗ, ꯈꯣꯡꯊꯥꯡ 11 ꯗ ꯕꯦꯠ $890 ꯑꯣꯏ ꯑꯃꯁꯨꯡ $2,320 ꯃꯥꯡꯂꯦ꯫ ꯃꯥꯏꯄꯥꯛꯄꯒꯤ ꯃꯇꯨꯡꯗ ꯅꯦꯠ ꯍꯥꯌꯕꯁꯤ ꯃꯃꯥꯡꯒꯤ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯏꯊꯤꯔꯕ ꯃꯇꯨꯡꯗ ꯈꯣꯡꯊꯥꯡ ꯑꯗꯨꯒꯤ ꯕꯦꯠ ꯃꯥꯏꯄꯥꯛꯂꯕꯗ ꯁ꯭ꯇ꯭ꯔꯤꯛ ꯑꯗꯨꯒꯤ ꯃꯍꯩꯅꯤ: ꯃꯥꯏꯄꯥꯛꯄ ꯑꯃꯅ ꯑꯔꯣꯏꯕ ꯃꯥꯏꯊꯤꯕ ꯑꯅꯤꯈꯛ ꯍꯜꯂꯛꯂꯤ, ꯍꯦꯟꯅꯥ ꯍꯜꯂꯀꯗꯦ꯫

ꯔꯨꯂꯦꯠ ꯇꯦꯕꯜꯒꯤ ꯉꯝꯈꯩꯁꯤꯡ

ꯁꯦꯁꯟ ꯑꯃꯥ ꯀꯔꯝꯕ ꯃꯑꯣꯡꯗ ꯎꯕꯒꯦ?

ꯑꯍꯧꯕ $10 ꯑꯃꯁꯨꯡ ꯁ꯭ꯄꯤꯟ ꯅꯤꯄꯥꯟ ꯂꯧꯕꯤꯌꯨ: L L W L L L W W꯫ ꯊꯝꯂꯕ ꯁꯦꯜꯁꯤꯡ 10, 10, 20 (ꯃꯥꯏꯄꯥꯛꯄ, ꯑꯅꯤ ꯍꯟꯊꯕ, ꯈꯣꯡꯊꯥꯡ 1 ꯗ), 10, 10, 20, 30 (ꯃꯥꯏꯄꯥꯛꯄ, ꯑꯅꯤ ꯍꯟꯊꯕ, ꯈꯣꯡꯊꯥꯡ 2 ꯗ), 10 (ꯃꯥꯏꯄꯥꯛꯄ, ꯍꯧꯔꯀꯐꯃꯗ) ꯑꯣꯏ꯫ ꯃꯥꯡꯈꯤꯕ: 10 + 10 + 10 + 10 + 20 = 60꯫ ꯃꯥꯏꯄꯥꯛꯈꯤꯕ: 20 + 30 + 10 = 60꯫ ꯃꯥꯏꯊꯤꯕ ꯃꯉꯥ, ꯃꯥꯏꯄꯥꯛꯄ ꯑꯍꯨꯝ, ꯑꯃꯁꯨꯡ ꯅꯍꯥꯛ ꯆꯞ ꯃꯥꯟꯅꯔꯦ꯫ ꯁꯤꯁ꯭ꯇꯦꯝ ꯑꯁꯤꯒꯤ ꯄꯥꯝꯖꯕꯥ ꯐꯕ ꯃꯑꯣꯡ ꯑꯗꯨ ꯃꯁꯤꯅꯤ꯫ ꯃꯃꯜ ꯑꯗꯨ ꯂꯥꯏꯟ ꯑꯗꯨꯃꯛꯇ ꯂꯩ: ꯃꯐꯝ ꯑꯗꯨꯗ ꯌꯧꯅꯕ $120 ꯒꯤ ꯕꯦꯠ ꯃꯊꯧ ꯇꯥꯈꯤ, ꯑꯃꯁꯨꯡ ꯊꯝꯂꯕ ꯗꯣꯂꯥꯔ ꯈꯨꯗꯤꯡꯃꯛꯅ ꯍꯥꯎꯁ ꯑꯦꯖꯃꯦꯊꯃꯦꯇꯤꯛꯁꯍꯥꯎꯁ ꯑꯦꯖꯊꯝꯂꯕ ꯁꯦꯜ ꯈꯨꯗꯤꯡꯗꯒꯤ ꯀꯦꯁꯤꯅꯣꯅ ꯑꯦꯚꯔꯦꯖꯗ ꯊꯃꯖꯤꯜꯂꯤꯕ ꯁꯔꯨꯛ: ꯌꯨꯔꯣꯄꯤꯌꯟ ꯔꯨꯂꯦꯠꯇ 2.70%꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯄꯨꯔꯤ꯫

ꯀꯔꯤꯒꯤ ꯈꯣꯡꯊꯥꯡ ꯑꯅꯤ ꯍꯟꯊꯕꯅꯣ, ꯑꯃꯈꯛ ꯅꯠꯇꯅ?

ꯃꯔꯃꯗꯤ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯃꯅ ꯆꯞꯆꯥꯅ ꯃꯥꯏꯊꯤꯕ ꯑꯅꯤꯒꯤ ꯃꯃꯜ ꯄꯤ꯫ ꯃꯁꯤꯡ ꯈꯨꯗꯤꯡꯃꯛ ꯃꯃꯥꯡꯒꯤ ꯃꯁꯤꯡ ꯑꯅꯤꯒꯤ ꯃꯄꯨꯡꯅꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯌꯨꯅꯤꯠ 5 ꯗ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯃꯅ ꯃꯃꯥꯡꯗ ꯃꯥꯡꯈꯤꯕ 2 ꯑꯃꯁꯨꯡ 3 ꯑꯗꯨ ꯍꯜꯂꯛꯂꯤ꯫ ꯈꯣꯡꯊꯥꯡ ꯂꯩꯕ ꯀꯥꯡꯂꯣꯟ ꯑꯃꯥ ꯈꯟꯕꯤꯌꯨ: ꯃꯥꯏꯊꯤꯕ ꯈꯨꯗꯤꯡꯃꯛꯇ ꯈꯣꯡꯊꯥꯡ ꯑꯃꯥ ꯀꯥꯏ, ꯃꯥꯏꯄꯥꯛꯄ ꯈꯨꯗꯤꯡꯃꯛꯇ ꯈꯣꯡꯊꯥꯡ ꯑꯅꯤ ꯇꯥꯏ꯫ ꯅꯍꯥꯛ ꯂꯦꯞꯂꯤꯕ ꯈꯣꯡꯊꯥꯡ ꯑꯗꯨ ꯅꯍꯥꯛꯀꯤ ꯁꯦꯜ ꯊꯤꯕꯅꯤ꯫ ꯈꯣꯡꯊꯥꯡ 5 ꯗ ꯅꯍꯥꯛ ꯌꯨꯅꯤꯠ 7 ꯃꯥꯡꯂꯦ, ꯈꯣꯡꯊꯥꯡ 8 ꯗ 33 ꯃꯥꯡꯂꯦ, ꯑꯃꯁꯨꯡ ꯑꯍꯥꯅꯕ ꯈꯣꯡꯊꯥꯡꯗ ꯍꯜꯂꯛꯂꯕꯗ ꯆꯞꯆꯥꯅ ꯆꯞ ꯃꯥꯟꯅꯔꯦ꯫ ꯀꯥꯟꯅꯕ ꯁꯦꯜ ꯑꯍꯥꯅꯕ ꯈꯣꯡꯊꯥꯡꯒꯤ ꯃꯥꯏꯄꯥꯛꯄꯁꯤꯡꯗꯒꯤ ꯈꯛꯇ ꯂꯥꯀꯏ, ꯑꯃꯨꯛꯇ ꯌꯨꯅꯤꯠ ꯑꯃꯥ꯫

ꯃꯥꯏꯄꯥꯛꯄ ꯑꯃꯁꯨꯡ ꯃꯥꯏꯊꯤꯕ ꯀꯌꯥ ꯃꯔꯥꯡ ꯆꯞ ꯃꯥꯟꯅꯕꯗ, ꯑꯃꯒꯤꯗꯃꯛ ꯈꯣꯡꯊꯥꯡ ꯑꯅꯤ ꯍꯥꯌꯕꯁꯤ ꯐꯕ ꯌꯦꯟ ꯑꯃꯥ ꯑꯣꯏꯅ ꯇꯥꯏ, ꯑꯃꯁꯨꯡ ꯃꯇꯝ ꯌꯥꯝꯅꯥ ꯀꯥꯡꯂꯣꯟ ꯑꯗꯨꯅ ꯇꯁꯦꯡꯅ ꯃꯈꯥꯗ ꯍꯜꯂꯀꯏ꯫ ꯑꯔꯥꯟ ꯈꯨꯕꯝ ꯑꯗꯨꯗꯤ ꯀꯥꯛꯂꯤꯉꯩꯗ ꯈꯣꯡꯊꯥꯡꯁꯤꯡ ꯍꯦꯟꯅꯥ ꯋꯥꯡꯂꯛꯂꯤ꯫ ꯑꯍꯥꯅꯕ ꯈꯣꯡꯊꯥꯡꯒꯤ ꯃꯥꯏꯄꯥꯛꯄ ꯇꯔꯥꯅ ꯌꯨꯅꯤꯠ 10 ꯄꯤ꯫ ꯈꯣꯡꯊꯥꯡ 6, 7 ꯑꯃꯁꯨꯡ 8 ꯒꯤ ꯃꯥꯏꯊꯤꯕ ꯑꯍꯨꯃꯅ 8 + 13 + 21 = 42 ꯃꯥꯡꯍꯜꯂꯤ꯫

ꯐꯤꯕꯣꯅꯥꯆꯤ ꯁꯦꯁꯟ ꯇꯔꯥ, ꯑꯍꯧꯕ $10, ꯉꯝꯈꯩ $500ꯍꯧꯔꯛꯐꯃꯒꯥ ꯆꯥꯡꯗꯝꯅꯕ ꯃꯍꯩ

ꯁꯦꯁꯟ 1,000 × ꯁ꯭ꯄꯤꯟ 500 · ꯃꯆꯨ ꯑꯃꯨ-ꯂꯩꯃꯜ p10/p25/p75/p90, ꯑꯉꯧ-ꯑꯁꯪꯕ ꯃꯤꯗꯤꯌꯥꯟ, ꯃꯌꯥꯏꯕ ꯈꯨꯗꯝ 82 · ꯁ꯭ꯄꯤꯟ ꯑꯃꯗ ꯀ꯭ꯕꯥꯟꯇꯥꯏꯜ ꯎꯅꯕ ꯆꯥꯔꯠꯀꯤ ꯃꯊꯛꯇ ꯃꯧꯁ ꯆꯠꯍꯅꯕꯤꯌꯨ

p10 −$500
p25 −$500
ꯃꯤꯗꯤꯌꯥꯟ −$500
p75 +$250
p90 +$920

ꯁꯦꯁꯟ 1,000 × ꯁ꯭ꯄꯤꯟ 500 · y-ꯑꯦꯛꯁꯤꯁ 1ꯁꯨꯕ–99ꯁꯨꯕ ꯄꯔꯁꯦꯟꯇꯥꯏꯜ ꯐꯥꯑꯣꯕꯥ ꯀꯛꯊꯠꯂꯤ (ꯑꯔꯣꯏꯕ ꯃꯁꯤꯡ −$500ꯗꯒꯤ +$1,400ꯐꯥꯑꯣꯕꯥ) · ꯁ꯭ꯄꯤꯟ 500 · ꯍꯧꯔꯛꯐꯝ $10 · ꯆꯞ ꯃꯥꯟꯅꯕ

ꯃꯥꯔꯇꯤꯟꯒꯦꯜꯗꯒꯤ ꯍꯦꯟꯅꯥ ꯇꯞꯅ ꯀꯥꯏ, ꯁꯤꯛꯋꯦꯟꯁ ꯑꯗꯨ ꯂꯥꯟꯊꯣꯛꯂꯕꯗ ꯍꯦꯟꯅꯥ ꯁꯥꯡꯅ ꯇꯥꯏ꯫

ꯐꯤꯕꯣꯅꯥꯆꯤ ꯁꯤꯁ꯭ꯇꯦꯝꯅ ꯊꯕꯛ ꯇꯧꯕ꯭ꯔꯥ?

ꯇꯧꯗꯦ꯫ ꯀꯥꯟꯅꯕꯗ ꯂꯣꯏꯁꯤꯟꯕꯒꯤ ꯂꯝꯕꯤ ꯑꯃꯥ ꯑꯣꯏꯅ ꯇꯧꯗꯦ꯫ ꯍꯤꯁꯥꯕ ꯑꯁꯤ ꯁꯤꯁ꯭ꯇꯦꯝ ꯈꯨꯗꯤꯡꯃꯛꯀꯤꯒꯨꯝꯅ ꯆꯞ ꯃꯥꯟꯅꯩ: ꯕꯦꯠ ꯈꯨꯗꯤꯡꯃꯛꯅ ꯑꯦꯚꯔꯦꯖꯗ ꯃꯁꯥꯒꯤ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ 1/37 ꯃꯥꯡꯏ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯁꯤꯛꯋꯦꯟꯁ ꯄꯨꯝꯅꯃꯛꯅ ꯊꯝꯂꯕ ꯄꯨꯝꯅꯃꯛꯀꯤ 1/37 ꯃꯥꯡꯏ꯫ ꯔꯨꯂꯦꯠꯇ ꯐꯤꯕꯣꯅꯥꯆꯤ ꯁꯤꯛꯋꯦꯟꯁ ꯁꯤꯖꯤꯟꯅꯕꯅ ꯃꯗꯨ ꯍꯣꯡꯗꯣꯀꯗꯦ, ꯃꯔꯃꯗꯤ ꯆꯤꯞꯁꯦꯜꯆꯤꯞꯂꯦꯞꯂꯕ ꯁꯦꯜꯒꯤ ꯃꯃꯜ ꯇꯥꯛꯄ ꯇꯣꯀꯟ, ꯕꯦꯠ ꯊꯝꯅꯕ ꯂꯦꯑꯥꯎꯠꯇ ꯊꯝꯃꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯆꯦꯛ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯗꯨ ꯀꯌꯥ ꯆꯥꯎꯔꯕꯁꯨ ꯆꯛꯔꯅ ꯑꯣꯗꯁ ꯑꯗꯨꯃꯛ ꯄꯤ꯫ ꯐꯤꯕꯣꯅꯥꯆꯤꯒꯤ ꯊꯝꯂꯕ ꯁꯦꯜꯁꯤꯡ ꯇꯞꯅ ꯍꯦꯅꯒꯠꯂꯛꯂꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯁꯤꯅ ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯗ ꯐ꯭ꯂꯦꯠ ꯕꯦꯇꯤꯡꯗꯒꯤꯊꯧꯔꯥꯡꯐ꯭ꯂꯦꯠ ꯕꯦꯇꯤꯡꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯗ ꯁꯦꯜ ꯃꯥꯟꯅꯕ ꯊꯝꯕ꯫ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯟ ꯈꯨꯗꯤꯡꯃꯛ ꯆꯥꯡꯗꯝꯅꯕ ꯃꯔꯨꯑꯣꯏꯕ ꯃꯈꯥꯌꯣꯜꯅꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯍꯦꯟꯅꯥ ꯊꯝꯃꯤ, ꯑꯃꯁꯨꯡ ꯁꯦꯁꯟ ꯈꯨꯗꯤꯡꯒꯤ ꯃꯁꯤꯒꯤ ꯃꯥꯡꯒꯗꯕ ꯁꯦꯜꯃꯦꯊꯃꯦꯇꯤꯛꯁꯃꯥꯡꯒꯗꯕ ꯁꯦꯜꯐꯪꯒꯗꯕ ꯃꯃꯂꯕꯨ ꯕꯦꯠ ꯊꯝꯂꯕ ꯁꯦꯜ ꯄꯨꯝꯅꯃꯛꯅ ꯃꯅꯥꯡꯕ; ꯁꯦꯁꯟ ꯅꯠꯔꯒ ꯃꯇꯝ ꯑꯃꯒꯤ ꯃꯅꯨꯡꯗ ꯃꯥꯡꯕ ꯑꯦꯚꯔꯦꯖ ꯁꯦꯜ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯍꯦꯟꯅꯥ ꯋꯥꯡꯏ꯫ ꯃꯥꯔꯇꯤꯟꯒꯦꯜꯅꯊꯧꯔꯥꯡꯃꯥꯔꯇꯤꯟꯒꯦꯜꯃꯥꯏꯊꯤꯕ ꯈꯨꯗꯤꯡꯒꯤ ꯃꯇꯨꯡꯗ ꯕꯦꯠ ꯑꯗꯨ ꯑꯅꯤ ꯊꯥꯛ ꯍꯦꯅꯒꯠꯍꯟꯕ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯟ꯫ ꯃꯁꯤꯅ ꯀꯔꯤ ꯇꯧꯕꯒꯦ ꯑꯃꯁꯨꯡ ꯀꯔꯤ ꯇꯧꯗꯕꯒꯦ ꯍꯥꯌꯕ ꯊꯧꯔꯥꯡꯒꯤ ꯁꯦꯛꯁꯅꯗ ꯌꯦꯡꯕꯤꯌꯨ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯃꯁꯤꯗꯒꯤꯁꯨ ꯍꯦꯟꯅꯥ ꯊꯝꯃꯤ, ꯑꯃꯁꯨꯡ ꯍꯦꯟꯅꯥ ꯃꯥꯡꯏ꯫

ꯐ꯭ꯂꯦꯠ ꯕꯦꯇꯤꯡ ꯔꯨꯂꯦꯠ ꯊꯧꯔꯥꯡ

ꯃꯁꯤ ꯃꯥꯔꯇꯤꯟꯒꯦꯜꯗꯒꯤ ꯍꯦꯟꯅꯥ ꯑꯁꯣꯏꯕ ꯌꯥꯎꯗꯕ꯭ꯔꯥ?

ꯃꯁꯤ ꯍꯦꯟꯅꯥ ꯇꯞꯏ, ꯃꯗꯨ ꯑꯃꯃꯛ ꯅꯠꯇꯦ꯫ ꯐꯤꯕꯣꯅꯥꯆꯤꯒꯤ ꯊꯝꯂꯕ ꯁꯦꯜꯁꯤꯡ ꯈꯣꯡꯊꯥꯡ ꯈꯨꯗꯤꯡꯗ 2× ꯅꯠꯇꯅ 1.6× ꯔꯣꯝ ꯍꯦꯅꯒꯠꯂꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯑꯍꯧꯕ $10 ꯗꯒꯤ $500 ꯉꯝꯈꯩꯗ ꯃꯈꯥ ꯆꯠꯅꯕ ꯃꯥꯏꯊꯤꯕ ꯇꯔꯨꯛ ꯅꯠꯇꯅ ꯇꯔꯥ ꯔꯣꯃꯒꯤ ꯃꯇꯨꯡꯗ ꯌꯧꯏ꯫ ꯃꯁꯤꯅ ꯆꯤꯡꯒꯤ ꯃꯊꯛ ꯑꯗꯨ ꯍꯦꯟꯅꯥ ꯈꯔꯥ ꯈꯛꯇ ꯊꯣꯀꯍꯜꯂꯤ: ꯃꯈꯥ ꯆꯠꯅꯕ ꯆꯞ ꯃꯥꯟꯅꯕ ꯃꯥꯏꯊꯤꯕ ꯇꯔꯥ ꯑꯁꯤ (19/37)¹⁰ ≈ 0.13% ꯅꯤ, ꯇꯔꯨꯛꯀꯤꯗꯃꯛ (19/37)⁶ ≈ 1.8%꯫ ꯑꯗꯨꯕꯨ ꯆꯤꯡꯒꯤ ꯃꯊꯛ ꯑꯗꯨꯁꯨ ꯍꯦꯟꯅꯥ ꯋꯥꯡꯏ, ꯃꯔꯃꯗꯤ ꯃꯐꯝ ꯑꯗꯨꯗ ꯌꯧꯗ꯭ꯔꯤꯉꯩꯗ ꯍꯦꯟꯅꯥ ꯊꯝꯂꯦ, ꯑꯃꯁꯨꯡ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯃꯈꯛꯅ ꯃꯗꯨ ꯍꯜꯂꯛꯍꯟꯕ ꯉꯝꯗꯦ꯫

ꯃꯥꯔꯇꯤꯟꯒꯦꯜꯐꯤꯕꯣꯅꯥꯆꯤ

ꯃꯥꯏꯊꯤꯕ ꯈꯨꯗꯤꯡꯗ ꯊꯝꯂꯕ ꯁꯦꯜ ꯍꯦꯅꯒꯠꯄ×2×1.62

$10 ꯗꯒꯤ $500 ꯌꯧꯅꯕ ꯃꯥꯏꯊꯤꯕ610

p(ꯃꯈꯥ ꯆꯠꯅꯕ ꯃꯥꯏꯊꯤꯕ ꯃꯗꯨꯃꯛ ꯀꯌꯥ)1.8%0.13%

ꯉꯝꯈꯩꯗ ꯃꯥꯡꯂꯕ ꯄꯨꯝꯅꯃꯛ$630$2,320 (ꯈꯣꯡꯊꯥꯡ 1–11)

ꯈꯣꯡꯊꯥꯡ 7 ꯗꯒꯤ ꯑꯃꯨꯛ ꯍꯟꯅꯥ ꯐꯪꯅꯕ ꯃꯊꯧ ꯇꯥꯕ ꯃꯥꯏꯄꯥꯛꯄ13

ꯃꯁꯤꯡꯁꯤꯡ ꯑꯁꯤ ꯀꯃꯗꯒꯤ ꯂꯥꯀꯄꯅꯣ?

ꯂꯝꯍꯥꯎꯁꯤꯡꯒꯤ ꯃꯔꯃꯗ ꯋꯥꯍꯜ ꯑꯃꯗꯒꯤ꯫ ꯃꯇꯨꯡꯗ ꯐꯤꯕꯣꯅꯥꯆꯤ ꯍꯥꯌꯅ ꯃꯃꯤꯡ ꯀꯧꯈꯤꯕ ꯄꯤꯁꯥꯒꯤ ꯂꯤꯑꯣꯅꯥꯔꯗꯣ (Leonardo of Pisa) ꯅ ꯃꯁꯤ 1202 ꯒꯤ ꯃꯍꯥꯛꯀꯤ ꯂꯤꯕꯦꯔ ꯑꯕꯥꯀꯤꯗ ꯊꯃꯈꯤ: ꯄꯦꯌꯔ ꯑꯃꯗꯒꯤ ꯍꯧꯔꯒ, ꯄꯦꯌꯔ ꯈꯨꯗꯤꯡꯃꯛꯅ ꯃꯁꯥꯒꯤ ꯑꯅꯤꯁꯨꯕ ꯊꯥꯗꯒꯤ ꯍꯧꯔꯒ ꯊꯥ ꯈꯨꯗꯤꯡꯗ ꯑꯅꯧꯕ ꯄꯦꯌꯔ ꯑꯃꯥ ꯄꯣꯀꯍꯟꯗꯨꯅ, ꯄꯦꯌꯔꯁꯤꯡ ꯃꯁꯤꯡ ꯊꯤꯕ꯫ ꯄꯥꯎꯈꯨꯝ ꯑꯗꯨ 1, 2, 3, 5, 8, 13 ꯑꯣꯏꯅ ꯆꯠꯂꯤ꯫ ꯅꯤꯌꯝ ꯑꯁꯤ ꯑꯍꯥꯅꯕ ꯑꯣꯏꯅ ꯊꯤꯈꯤꯕꯁꯤ ꯃꯍꯥꯛ ꯅꯠꯇꯦ꯫ ꯁꯩꯔꯦꯡꯒꯤ ꯇꯥꯜ ꯇꯝꯂꯤꯕ ꯏꯟꯗꯤꯌꯥꯒꯤ ꯃꯍꯩꯔꯣꯏꯁꯤꯡꯅ ꯃꯃꯥꯡꯗ ꯏꯈꯤꯔꯦ: ꯁꯤꯡ (Singh) (1985) ꯅ ꯃꯁꯤ 600 ꯑꯃꯁꯨꯡ 800 ꯒꯤ ꯃꯔꯛꯇ ꯂꯩꯈꯤꯕ ꯚꯤꯔꯍꯥꯡꯀ ꯐꯥꯑꯣꯕ, ꯃꯗꯨꯒꯤ ꯃꯇꯨꯡꯗ ꯒꯣꯄꯥꯜ ꯑꯃꯁꯨꯡ ꯍꯦꯃꯆꯟꯗ꯭ꯔ ꯐꯥꯑꯣꯕ ꯊꯤꯗꯣꯛꯂꯤ꯫

ꯃꯈꯣꯌꯒꯤ ꯃꯔꯛꯇ ꯀꯅꯥꯒꯨꯝꯕ ꯑꯃꯠꯇꯅ ꯆꯛꯔ ꯑꯃꯥ ꯋꯥꯈꯂꯗ ꯊꯃꯈꯤꯗꯦ꯫ ꯃꯐꯝ ꯑꯁꯤꯗ ꯁꯤꯖꯤꯟꯅꯔꯤꯕ ꯍꯧꯔꯀꯐꯃꯁꯤꯡꯅ ꯁꯤꯛꯋꯦꯟꯁ ꯑꯁꯤꯒꯤ ꯃꯇꯨꯡ ꯏꯟꯅ ꯑꯍꯥꯅꯕ ꯑꯣꯏꯅ ꯁꯦꯜ ꯊꯃꯈꯤꯕꯁꯤ ꯀꯅꯥꯅꯣ ꯍꯥꯌꯕꯗꯦ꯫ ꯃꯈꯣꯌꯅ ꯎꯠꯂꯤꯕꯗꯤ ꯃꯁꯤꯒꯤ ꯍꯤꯁꯥꯕ ꯑꯃꯁꯨꯡ ꯔꯨꯂꯦꯠꯀꯤ ꯍꯤꯁꯥꯕ ꯀꯩꯗꯧꯉꯩꯗꯁꯨ ꯎꯅꯗꯦ: ꯑꯃꯅ ꯊꯝꯂꯕ ꯁꯦꯜꯁꯤꯡ ꯀꯔꯝꯅ ꯍꯦꯅꯒꯠꯂꯛꯀꯅꯤ ꯍꯥꯌꯏ, ꯑꯇꯣꯞꯄꯅ ꯊꯝꯂꯕ ꯁꯦꯜ ꯈꯨꯗꯤꯡꯃꯛꯅ ꯀꯔꯤ ꯍꯜꯂꯀꯄꯒꯦ ꯍꯥꯌꯏ꯫

ꯂꯝꯍꯥꯎ ꯌꯨꯝ ꯈꯨꯗꯤꯡꯃꯛ ꯍꯦꯟꯅꯥ ꯊꯟꯊꯔꯛꯂꯤꯉꯩꯗ ꯄꯤꯁꯥꯒꯤ ꯂꯤꯑꯣꯅꯥꯔꯗꯣꯅ ꯂꯝꯍꯥꯎ ꯄꯦꯌꯔꯁꯤꯡ ꯃꯁꯤꯡ ꯊꯤꯔꯤ꯫

ꯃꯥꯏꯊꯤꯕꯒꯤ ꯁ꯭ꯇ꯭ꯔꯤꯛ ꯑꯃꯒꯤ ꯃꯇꯨꯡꯗ ꯀꯌꯥ ꯃꯥꯡꯕꯒꯦ?

ꯑꯥꯏꯗꯦꯟꯇꯤꯇꯤ ꯑꯅꯤꯅ ꯃꯊꯛꯇ ꯂꯩꯕ ꯇꯦꯕꯜ ꯑꯗꯨ ꯌꯦꯡꯁꯤꯟꯕ ꯂꯥꯏꯍꯜꯂꯤ꯫ ꯃꯈꯥ ꯆꯠꯅꯕ ꯃꯥꯏꯊꯤꯕ n ꯒꯤ ꯃꯇꯨꯡꯗ ꯃꯥꯡꯂꯕ ꯄꯨꯝꯅꯃꯛ ꯑꯁꯤ (n + 2) ꯁꯨꯕ ꯐꯤꯕꯣꯅꯥꯆꯤ ꯃꯁꯤꯡꯗꯒꯤ 1 ꯂꯧꯊꯣꯛꯂꯕꯅꯤ, ꯃꯁꯤꯅ 1, 2, 4, 7, 12, 20 ꯑꯁꯤꯅ ꯆꯠꯂꯤ, ꯑꯃꯁꯨꯡ ꯃꯊꯪꯒꯤ ꯊꯝꯂꯕ ꯁꯦꯜ ꯑꯁꯤ (n + 1) ꯁꯨꯕ ꯐꯤꯕꯣꯅꯥꯆꯤ ꯃꯁꯤꯡꯅꯤ꯫ ꯕꯣꯜꯃꯦꯟ (Bollman) (2021) ꯅ 1, 2, 3 ꯗꯒꯤ ꯍꯧꯕ ꯁꯤꯛꯋꯦꯟꯁ ꯑꯃꯒꯤꯗꯃꯛ ꯏꯟꯗꯛꯁꯅꯅ ꯃꯍꯩ ꯑꯗꯨꯃꯛ ꯄ꯭ꯔꯨꯐ ꯇꯧꯏ, ꯃꯁꯤꯅ ꯃꯁꯤꯡ ꯈꯨꯗꯤꯡꯃꯛ ꯃꯐꯝ ꯑꯃꯥ ꯆꯦꯟꯊꯍꯜꯂꯤ꯫ ꯌꯨꯅꯤꯠ 1 ꯗꯒꯤ ꯍꯧꯔꯒ ꯌꯨꯅꯤꯠ 500 ꯒꯤ ꯉꯝꯈꯩꯗ, ꯃꯥꯔꯇꯤꯟꯒꯦꯜꯅ ꯃꯁꯥꯒꯤ 10 ꯁꯨꯕ ꯕꯦꯠ, ꯌꯨꯅꯤꯠ 512, ꯊꯝꯕ ꯉꯝꯗꯦ꯫ ꯐꯤꯕꯣꯅꯥꯆꯤꯅ ꯃꯁꯥꯒꯤ 14 ꯁꯨꯕ, ꯌꯨꯅꯤꯠ 377, ꯊꯝꯕ ꯉꯝꯃꯤ, ꯑꯗꯨꯕꯨ 15 ꯁꯨꯕ, 610, ꯊꯝꯕ ꯉꯝꯗꯦ꯫

ꯃꯥꯔꯇꯤꯟꯒꯦꯜꯐꯤꯕꯣꯅꯥꯆꯤ

500 ꯒꯤ ꯃꯈꯥꯒꯤ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯆꯥꯎꯕ ꯕꯦꯠ256 (ꯕꯦꯠ 9 ꯁꯨꯕ)377 (ꯕꯦꯠ 14 ꯁꯨꯕ)

ꯃꯁꯤꯕꯨ ꯊꯨꯒꯥꯏꯕ ꯃꯈꯥ ꯆꯠꯅꯕ ꯃꯥꯏꯊꯤꯕ914

ꯃꯇꯝ ꯑꯗꯨ ꯐꯥꯑꯣꯕ ꯃꯥꯡꯂꯕ ꯌꯨꯅꯤꯠ511986

ꯑꯉꯥꯡꯕꯗ ꯈꯨꯗꯣꯡꯆꯥꯕ, ꯁ꯭ꯄꯤꯟ ꯑꯃꯗꯒꯤ ꯍꯧꯔꯒ0.25%0.0089%

ꯌꯨꯅꯤꯠ 1 ꯗꯒꯤ ꯍꯧꯕ, ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯋꯥꯡꯕ ꯌꯨꯅꯤꯠ 500, ꯌꯨꯔꯣꯄꯤꯌꯟ ꯆꯛꯔ꯫

ꯗꯖꯟ ꯅꯠꯔꯒ ꯀꯂꯝ ꯑꯃꯗ ꯀꯔꯤ ꯍꯣꯡꯕꯒꯦ?

2 ꯗꯒꯤ 1 ꯄꯤꯕ ꯗꯖꯟꯕꯦꯠꯗꯖꯟ1–12, 13–24 ꯅꯠꯔꯒ 25–36, 2:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯅꯠꯔꯒ ꯀꯂꯝꯕꯦꯠꯀꯂꯝꯂꯦꯑꯥꯎꯠꯀꯤ ꯊꯣꯡꯅꯥꯡꯒꯤ ꯀꯂꯝ ꯑꯃꯗ ꯂꯩꯕ ꯃꯁꯤꯡ ꯇꯔꯥꯅꯤꯊꯣꯏ, 2:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯗ ꯃꯇꯨꯡꯗ ꯍꯟꯊꯕ ꯃꯊꯧ ꯇꯥꯗꯦ꯫ ꯊꯝꯂꯕ ꯁꯦꯜ F ꯗ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯃꯅ 2F ꯄꯤ, ꯃꯁꯤ ꯃꯃꯥꯡꯗ ꯃꯥꯡꯈꯤꯕ ꯄꯨꯝꯅꯃꯛꯇꯒꯤ ꯃꯇꯝ ꯄꯨꯝꯕꯗ ꯍꯦꯟꯅꯥ ꯋꯥꯡꯏ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯥꯏꯄꯥꯛꯄ ꯈꯨꯗꯤꯡꯃꯛꯅ ꯁꯤꯛꯋꯦꯟꯁ ꯑꯗꯨ ꯀꯥꯟꯅꯕꯗ ꯂꯣꯏꯁꯤꯜꯂꯤ꯫ ꯃꯃꯜ ꯑꯗꯨꯗꯤ ꯗꯖꯟ ꯑꯃꯅ 37 ꯗ 12 ꯈꯛ ꯃꯥꯏꯄꯥꯛꯏ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯁꯥꯡꯂꯕ ꯃꯥꯏꯊꯤꯕꯒꯤ ꯁ꯭ꯇ꯭ꯔꯤꯛꯁꯤꯡ ꯌꯥꯝꯅ ꯍꯦꯟꯅꯥ ꯊꯣꯀꯏ: ꯃꯈꯥ ꯆꯠꯅꯕ ꯗꯖꯟ ꯃꯥꯏꯊꯤꯕ ꯇꯔꯥꯃꯔꯤ ꯑꯁꯤ ꯍꯣꯠꯅꯕ 242 ꯗ ꯑꯃꯨꯛ ꯔꯣꯝ ꯊꯣꯀꯏ, ꯑꯉꯥꯡꯕꯒꯤꯗꯃꯛꯕꯦꯠꯑꯉꯥꯡꯕꯑꯉꯥꯡꯕ ꯃꯁꯤꯡ 18 ꯗ ꯊꯝꯕ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠ꯫ ꯐ꯭ꯔꯦꯟꯆ: ꯔꯨꯖ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → 11,000 ꯗ ꯑꯃꯨꯛ ꯔꯣꯝ꯫

ꯕꯦꯠꯃꯃꯥꯡꯗ ꯃꯥꯡꯈꯤꯕꯊꯝꯂꯕ ꯁꯦꯜꯃꯥꯏꯄꯥꯛꯄꯒꯤ ꯃꯇꯨꯡꯗ ꯅꯦꯠ

101+2

211+1

322+2

443+2

575+3

6128+4

72013+6

83321+9

95434+14

108855+22

ꯃꯈꯥ ꯆꯠꯅꯕ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯅꯤꯒꯤ ꯃꯇꯨꯡꯗ ꯈꯛꯇ ꯂꯦꯞꯂꯕꯗꯗꯤ ꯀꯔꯝꯅꯣ?

ꯑꯇꯣꯞꯄ ꯃꯈꯜ ꯑꯃꯅ ꯃꯥꯏꯄꯥꯛꯂꯕꯁꯨ ꯃꯥꯏꯊꯤꯔꯕꯁꯨ ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯃꯛꯀꯤ ꯃꯇꯨꯡꯗ ꯈꯣꯡꯊꯥꯡ ꯑꯃꯥ ꯃꯃꯥꯡꯗ ꯆꯠꯂꯤ, ꯑꯃꯁꯨꯡ ꯃꯈꯥ ꯆꯠꯅꯕ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯅꯤꯒꯤ ꯃꯇꯨꯡꯗ ꯈꯛꯇ ꯂꯦꯞꯂꯤ꯫ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯅꯤꯒꯤ ꯃꯃꯥꯡꯗ ꯃꯥꯏꯊꯤꯕ n ꯂꯩꯔꯕꯗ, ꯀꯥꯟꯅꯕ ꯁꯦꯜ ꯑꯁꯤ (n + 1) ꯁꯨꯕ ꯐꯤꯕꯣꯅꯥꯆꯤ ꯃꯁꯤꯡꯗ 1 ꯍꯥꯄꯆꯤꯜꯂꯕꯅꯤ: ꯃꯥꯏꯄꯥꯛꯄꯁꯤꯡ ꯊꯨꯅ ꯂꯥꯀꯄꯗ ꯑꯄꯤꯛꯄ, ꯃꯇꯨꯡꯗ ꯂꯥꯀꯄꯗ ꯍꯦꯟꯅꯥ ꯆꯥꯎꯕ, ꯑꯃꯁꯨꯡ ꯃꯗꯨꯒꯥ ꯆꯥꯅꯕ ꯑꯣꯏꯅ ꯍꯦꯅꯒꯠꯂꯛꯂꯕ ꯊꯝꯂꯕ ꯁꯦꯜꯁꯤꯡꯗ ꯃꯥꯏꯄꯥꯛꯏ꯫ ꯊꯨꯅ ꯂꯥꯀꯄ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯅꯤ ꯃꯇꯝ ꯄꯨꯝꯕꯗ ꯑꯄꯤꯛꯄ ꯊꯝꯂꯕ ꯁꯦꯜꯗ ꯂꯥꯀꯏ; ꯃꯇꯨꯡꯗ ꯂꯥꯀꯄ ꯑꯅꯤꯅ ꯁꯦꯁꯟ ꯑꯗꯨ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯐꯠꯇꯕ ꯃꯇꯝ ꯑꯗꯨꯃꯛꯇ ꯑꯆꯧꯕ ꯕꯦꯠ ꯑꯃꯥ ꯃꯊꯧ ꯇꯥꯍꯅꯕ ꯌꯥꯏ꯫

ꯃꯥꯏꯄꯥꯛꯄ ꯑꯅꯤꯒꯤ ꯃꯃꯥꯡꯒꯤ ꯃꯥꯏꯊꯤꯕꯑꯔꯣꯏꯕ ꯃꯥꯏꯄꯥꯛꯄꯗ ꯊꯝꯂꯕ ꯁꯦꯜꯀꯥꯟꯅꯕ ꯁꯦꯜ

01+2

12+2

23+3

35+4

48+6

513+9

621+14

734+22

ꯁꯤꯛꯋꯦꯟꯁ 1, 1, 2, 3, 5, 8… ꯂꯃꯥꯏ ꯑꯁꯤꯗ ꯂꯩꯕꯒꯨꯝ꯫

ꯁꯤꯃꯨꯂꯦꯇꯔ · ꯐꯤꯕꯣꯅꯥꯆꯤ

$1,000ꯒꯤ ꯕꯦꯡꯀꯔꯣꯜꯗꯒꯤ ꯍꯧꯔꯒꯥ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠꯁꯤꯡꯒꯤ ꯁꯦꯁꯟ 2,000꯫

ꯍꯧꯔꯛꯐꯃꯒꯤ ꯕꯦꯠ $10 · ꯇꯦꯕꯜꯒꯤ ꯉꯝꯈꯩ $500 · ꯁꯦꯁꯟ ꯈꯨꯗꯤꯡꯗ ꯁ꯭ꯄꯤꯟ 100

ꯁꯦꯁꯟꯒꯤ ꯃꯍꯩꯁꯤꯡꯒꯤ ꯗꯤꯁ꯭ꯇ꯭ꯔꯤꯕ꯭ꯌꯨꯁꯟꯃꯥꯡꯕ ← | → ꯀꯥꯟꯅꯕ

−$1,000$0+$410

ꯕꯥꯔ ꯑꯃꯒꯤ ꯃꯊꯛꯇ ꯃꯧꯁ ꯊꯝꯕꯤꯌꯨ · ꯑꯉꯥꯡꯕ ꯕꯥꯔꯁꯤꯡ ꯑꯁꯤ ꯃꯥꯏꯊꯤꯕ ꯁꯦꯁꯟꯁꯤꯡꯅꯤ, ꯑꯁꯪꯕꯁꯤꯡ ꯃꯥꯏꯄꯥꯛꯄ, ꯃꯆꯨ ꯃꯌꯥꯏꯕ ꯕꯥꯔ ꯑꯗꯨꯅ $0 ꯌꯥꯎꯏ

ꯀꯥꯟꯅꯕ ꯐꯪꯂꯕ ꯁꯦꯁꯟꯁꯤꯡ

73.6%

ꯃꯤꯗꯤꯌꯥꯟ ꯃꯍꯩ

+$150

ꯑꯦꯚꯔꯦꯖ ꯃꯍꯩ

−$70.64

ꯕꯦꯡꯀꯔꯣꯜ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯡꯈꯤꯕ

17.8%

5ꯁꯨꯕ ꯄꯔꯁꯦꯟꯇꯥꯏꯜ

−$1,000

ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯋꯥꯡꯕ ꯗ꯭ꯔꯣꯗꯥꯎꯅꯒꯤ ꯃꯤꯗꯤꯌꯥꯟ

−$330

ꯃꯥꯏꯊꯤꯕ ꯁ꯭ꯇ꯭ꯔꯤꯛ ꯀꯌꯥ ꯌꯥꯝꯅ ꯂꯥꯀꯄꯒꯦ

ꯁꯤꯡꯒꯜ ꯖꯤꯔꯣ ꯆꯛꯔ ꯑꯃꯗ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠ ꯑꯃꯅ ꯁ꯭ꯄꯤꯟ 37 ꯈꯨꯗꯤꯡꯗ 19 ꯃꯥꯏꯊꯤ꯫ ꯔꯣ ꯈꯨꯗꯤꯡꯃꯛꯅ ꯁ꯭ꯄꯤꯟ ꯀꯌꯥ ꯄꯨꯝꯅꯃꯛ ꯃꯥꯏꯊꯤꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯑꯃꯁꯨꯡ ꯃꯥꯏꯊꯤꯕ ꯈꯨꯗꯤꯡꯃꯛꯀꯤ ꯃꯇꯨꯡꯗ ꯁꯤꯛꯋꯦꯟꯁꯇ ꯈꯣꯡꯊꯥꯡ ꯑꯃꯥ ꯆꯠꯂꯤꯕ ꯐꯤꯕꯣꯅꯥꯆꯤ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯅ ꯃꯇꯝ ꯑꯗꯨ ꯐꯥꯑꯣꯕꯥ ꯃꯥꯡꯈꯤꯕ ꯁꯦꯜ ꯎꯠꯂꯤ꯫

ꯍꯧꯔꯛꯐꯃꯒꯤ ꯕꯦꯠ

ꯃꯊꯪ ꯃꯊꯪ ꯃꯥꯏꯊꯤꯕ	ꯈꯨꯗꯣꯡꯆꯥꯕ	ꯃꯇꯧ ꯑꯁꯤꯒꯨꯝꯅ 1 / …	ꯍꯧꯖꯤꯛ ꯐꯥꯑꯣꯕꯥ ꯃꯥꯡꯈꯤꯕ	ꯃꯊꯪꯒꯤ ꯕꯦꯠ
1	51.4%	2	$1	$1
2	26.4%	4	$2	$2
3	13.5%	7	$4	$3
4	7.0%	14	$7	$5
5	3.6%	28	$12	$8
6	1.8%	55	$20	$13
7	0.94%	106	$33	$21
8	0.48%	207	$54	$34
9	0.25%	403	$88	$55
10	0.13%	784	$143	$89
11	0.065%	1527	$232	$144
12	0.034%	2974	$376	$233
13	0.017%	5792	$609	$377
14	0.0089%	11279	$986	$610
15	0.0046%	21965	$1,596	$987

ꯈꯨꯗꯣꯡꯆꯥꯕ ꯑꯁꯤ ꯃꯥꯏꯊꯤꯕ ꯑꯃꯗ ꯑꯃꯨꯛ 19/37 ꯃꯁꯥꯃꯛꯀꯥ ꯃꯜꯇꯤꯞꯂꯥꯏ ꯇꯧꯕꯅꯤ, ꯈꯅꯕ ꯁ꯭ꯄꯤꯟ ꯑꯃꯗꯒꯤ ꯍꯧꯔꯒꯥ ꯊꯤꯕ꯫ ꯁꯥꯡꯕ ꯁꯦꯁꯟ ꯑꯃꯗ ꯑꯁꯤꯒꯨꯝꯕ ꯁ꯭ꯇ꯭ꯔꯤꯛ ꯍꯧꯕ ꯌꯥꯕ ꯁ꯭ꯄꯤꯟ ꯀꯌꯥ ꯂꯩ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯅꯨꯃꯤꯗꯥꯡ ꯑꯃꯒꯤ ꯃꯅꯨꯡꯗ ꯃꯁꯤ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯔꯣ ꯑꯃꯅ ꯎꯠꯂꯤꯕꯗꯒꯤ ꯌꯥꯝꯅ ꯍꯦꯟꯅꯥ ꯋꯥꯡꯏ꯫

ꯋꯥꯍꯪꯁꯤꯡ

“ꯔꯤꯚꯔꯁ ꯐꯤꯕꯣꯅꯥꯆꯤ” ꯂꯩꯕ꯭ꯔꯥ?

ꯂꯩ: ꯃꯥꯏꯄꯥꯛꯄꯒꯤ ꯃꯇꯨꯡꯗ ꯃꯃꯥꯡꯗ, ꯃꯥꯏꯊꯤꯕꯒꯤ ꯃꯇꯨꯡꯗ ꯃꯇꯨꯡꯗ꯫ ꯃꯁꯤ ꯍꯦꯟꯅꯥ ꯇꯞꯄ ꯄꯥꯔꯣꯂꯤꯊꯧꯔꯥꯡꯄꯥꯔꯣꯂꯤꯄꯣꯖꯤꯇꯤꯕ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯟ: ꯃꯥꯏꯄꯥꯛꯂꯕꯥ ꯃꯇꯨꯡꯗ ꯑꯅꯤ ꯊꯥꯛ ꯍꯦꯅꯒꯠꯍꯜꯂꯤ, ꯃꯥꯏꯊꯤꯔꯕꯥ ꯃꯇꯨꯡꯗ ꯅꯠꯔꯒ ꯃꯈꯥ ꯆꯠꯅꯅ ꯑꯃꯨꯛ ꯑꯍꯨꯝ ꯃꯥꯏꯄꯥꯛꯂꯕꯥ ꯃꯇꯨꯡꯗ ꯑꯍꯧꯕꯗ ꯍꯜꯂꯀꯏ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯔꯤꯚꯔꯁ ꯃꯥꯔꯇꯤꯟꯒꯦꯜ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯒꯨꯝ ꯆꯠꯂꯤ꯫

ꯃꯦꯊꯃꯦꯇꯤꯛꯁꯀꯥ ꯁꯥꯟꯅꯕ

ꯃꯁꯤꯁꯤꯡ ꯑꯍꯥꯅꯕꯗ ꯅꯍꯥꯛ ꯃꯁꯥꯃꯛꯅ ꯍꯣꯠꯅꯕꯤꯌꯨ꯫ ꯄꯥꯎꯈꯨꯝ ꯈꯨꯗꯤꯡꯃꯛ ꯊꯨꯡꯗꯨꯅ ꯊꯝꯂꯤ; ꯁꯦꯝ ꯁꯥꯔꯕ ꯃꯇꯃꯗ ꯍꯥꯡꯗꯣꯛꯄꯤꯌꯨ꯫

ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯒꯤ ꯃꯇꯨꯡꯗ, ꯃꯥꯏꯄꯥꯛꯂꯕꯁꯨ ꯃꯥꯏꯊꯤꯔꯕꯁꯨ, ꯁꯤꯛꯋꯦꯟꯁ ꯑꯗꯨꯗ ꯈꯣꯡꯊꯥꯡ ꯑꯃꯥ ꯆꯠꯄ ꯑꯃꯁꯨꯡ ꯃꯈꯥ ꯆꯠꯊꯅ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯅꯤꯒꯤ ꯃꯇꯨꯡꯗ ꯂꯦꯞꯄ ꯃꯈꯜ ꯑꯗꯨ ꯁꯥꯟꯅꯕꯤꯌꯨ: ꯊꯝꯂꯕ ꯁꯦꯜ 1, 1, 2, 3, 5, 8 ꯑꯁꯤꯅꯆꯤꯡꯕ꯫ ꯑꯍꯥꯅꯕ ꯃꯍꯩ ꯇꯔꯥꯃꯔꯤ ꯑꯁꯤꯅꯤ: ꯃꯥꯏꯄꯥꯛ ꯃꯥꯏꯊꯤ ꯃꯥꯏꯄꯥꯛ ꯃꯥꯏꯊꯤ ꯃꯥꯏꯊꯤ ꯃꯥꯏꯊꯤ ꯃꯥꯏꯄꯥꯛ ꯃꯥꯏꯊꯤ ꯃꯥꯏꯊꯤ ꯃꯥꯏꯊꯤ ꯃꯥꯏꯄꯥꯛ ꯃꯥꯏꯊꯤ ꯃꯥꯏꯊꯤ ꯃꯥꯏꯄꯥꯛ꯫ ꯅꯍꯥꯛ ꯀꯗꯥꯏꯗ ꯂꯩꯔꯤꯕꯒꯦ, ꯑꯃꯁꯨꯡ ꯃꯊꯪꯒꯤ ꯕꯦꯠ ꯑꯗꯨ ꯀꯌꯥꯅꯣ?
ꯄꯥꯎꯈꯨꯝ ꯎꯠꯄ
ꯄꯥꯎꯈꯨꯝ ꯌꯨꯅꯤꯠꯁꯦꯜꯌꯨꯅꯤꯠꯁꯤꯁ꯭ꯇꯦꯝ ꯅꯠꯔꯒ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯅ ꯁꯤꯖꯤꯟꯅꯕ ꯃꯔꯨꯑꯣꯏꯕ ꯊꯝꯂꯕ ꯁꯦꯜ꯫ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯅꯁꯤꯡ ꯌꯨꯅꯤꯠꯇ ꯁꯟꯗꯣꯛꯂꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯈꯣꯌ ꯀꯔꯤꯒꯨꯝꯕ ꯇꯦꯕꯜꯗ ꯆꯠꯂꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → 22 ꯃꯥꯡꯂꯤ꯫ ꯃꯊꯪꯒꯤ ꯕꯦꯠ ꯑꯗꯨ ꯌꯨꯅꯤꯠ 610 ꯅꯤ, ꯑꯃꯁꯨꯡ ꯃꯥꯏꯄꯥꯛꯂꯕꯗ ꯁꯦꯁꯟ ꯑꯗꯨ 588 ꯀꯥꯟꯗꯨꯅ ꯂꯣꯏꯁꯤꯅꯒꯅꯤ꯫
ꯊꯝꯂꯕ ꯁꯦꯜꯁꯤꯡ ꯑꯗꯨ ꯑꯍꯥꯅꯕ ꯐꯤꯕꯣꯅꯥꯆꯤꯊꯧꯔꯥꯡꯐꯤꯕꯣꯅꯥꯆꯤ1, 1, 2, 3, 5, 8, 13… ꯁꯤꯛꯋꯦꯟꯁ ꯃꯇꯨꯡ ꯏꯟꯕ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯟ: ꯃꯥꯏꯊꯤꯔꯕꯥ ꯃꯇꯨꯡꯗ ꯈꯣꯡꯊꯥꯡ ꯑꯃꯥ ꯃꯃꯥꯡꯗ, ꯃꯥꯏꯄꯥꯛꯂꯕꯥ ꯃꯇꯨꯡꯗ ꯈꯣꯡꯊꯥꯡ ꯑꯅꯤ ꯃꯇꯨꯡꯗ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯃꯁꯤꯡ ꯇꯔꯥꯃꯔꯤꯅꯤ: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 ꯑꯃꯁꯨꯡ 377꯫ ꯃꯥꯏꯄꯥꯛꯄꯁꯤꯡ ꯄꯨꯟꯁꯤꯟꯕꯤꯌꯨ ꯑꯃꯁꯨꯡ ꯃꯥꯏꯊꯤꯕꯁꯤꯡ ꯂꯧꯊꯣꯀꯄꯤꯌꯨ: +1 −1 +2 −3 −5 −8 +13 −21 −34 −55 +89 −144 −233 +377 = −22꯫
ꯑꯔꯣꯏꯕ ꯃꯍꯩ ꯑꯗꯨ ꯃꯥꯏꯄꯥꯛꯄꯅꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯃꯥ ꯍꯦꯟꯅꯥ ꯐꯪꯂꯕꯗ ꯂꯣꯏꯁꯤꯅꯒꯅꯤ꯫ ꯃꯊꯪꯒꯤ ꯊꯝꯂꯕ ꯁꯦꯜ 610 ꯅꯤ: ꯃꯥꯏꯄꯥꯛꯂꯕꯗ +588 ꯊꯃꯏ, ꯃꯥꯏꯊꯤꯔꯕꯗ −632 ꯑꯃꯁꯨꯡ ꯃꯊꯪꯒꯤ ꯊꯝꯂꯕ ꯁꯦꯜ 987 ꯊꯃꯏ꯫
ꯃꯈꯜ ꯑꯁꯤ ꯃꯇꯝ ꯄꯨꯝꯅꯃꯛꯇ ꯀꯥꯟꯗꯨꯅ ꯂꯣꯏꯁꯤꯜꯂꯤ, ꯑꯗꯨꯕꯨ ꯃꯐꯝ ꯑꯁꯤꯗ ꯃꯗꯨ ꯇꯧꯅꯕꯒꯤꯗꯃꯛ ꯌꯨꯅꯤꯠ 610 ꯒꯤ ꯕꯦꯠ ꯃꯊꯧ ꯇꯥꯏ꯫ ꯃꯍꯧꯁꯥꯒꯤ ꯅꯤꯌꯝꯁꯤꯡꯗ, ꯃꯥꯏꯄꯥꯛꯄꯒꯤ ꯃꯇꯨꯡꯗ ꯈꯣꯡꯊꯥꯡ ꯑꯅꯤ ꯍꯜꯂꯛꯄꯗ, ꯃꯍꯩ ꯇꯔꯥꯃꯔꯤ ꯑꯗꯨꯅ ꯅꯍꯥꯛꯄꯨ ꯌꯨꯅꯤꯠ 1 ꯈꯛ ꯃꯥꯡꯍꯜꯂꯤ ꯑꯃꯁꯨꯡ ꯃꯊꯪꯒꯤ ꯕꯦꯠ 2 ꯑꯣꯏ꯫ ꯁꯤꯛꯋꯦꯟꯁ ꯑꯗꯨ 1, 2, 3 ꯗꯒꯤ ꯍꯧꯕ ꯕꯣꯂꯃꯦꯟ (2021) ꯅ 1 ꯃꯥꯡꯕ ꯑꯃꯁꯨꯡ ꯃꯊꯪꯒꯤ ꯕꯦꯠ 3 ꯐꯪꯏ꯫ ꯃꯍꯧꯁꯥꯒꯤ ꯅꯤꯌꯝꯁꯤꯡꯅ ꯃꯐꯝ ꯑꯁꯤꯗ ꯍꯦꯟꯅꯥ ꯅꯦꯝꯅ ꯃꯥꯡꯏ ꯃꯔꯃꯗꯤ ꯃꯥꯏꯄꯥꯛꯄ ꯈꯨꯗꯤꯡꯃꯛꯅ ꯊꯝꯂꯕ ꯁꯦꯜꯁꯤꯡ ꯍꯟꯅꯥ ꯍꯟꯊꯍꯜꯂꯤ꯫
ꯁ꯭ꯄꯤꯟꯊꯝꯂꯕ ꯁꯦꯜꯃꯍꯩꯆꯠꯂꯤꯕ ꯄꯨꯝꯅꯃꯛ
11ꯃꯥꯏꯄꯥꯛꯄ+1
21ꯃꯥꯏꯊꯤꯕ0
32ꯃꯥꯏꯄꯥꯛꯄ+2
43ꯃꯥꯏꯊꯤꯕ−1
55ꯃꯥꯏꯊꯤꯕ−6
68ꯃꯥꯏꯊꯤꯕ−14
713ꯃꯥꯏꯄꯥꯛꯄ−1
821ꯃꯥꯏꯊꯤꯕ−22
934ꯃꯥꯏꯊꯤꯕ−56
1055ꯃꯥꯏꯊꯤꯕ−111
1189ꯃꯥꯏꯄꯥꯛꯄ−22
12144ꯃꯥꯏꯊꯤꯕ−166
13233ꯃꯥꯏꯊꯤꯕ−399
14377ꯃꯥꯏꯄꯥꯛꯄ−22
ꯃꯇꯧ ꯑꯁꯨꯝꯕ ꯃꯈꯜ ꯑꯗꯨꯗ, ꯃꯥꯏꯊꯤꯕ n ꯒꯤ ꯃꯇꯨꯡꯗ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯅꯤꯅ ꯀꯔꯤꯒꯤ ꯃꯇꯝ ꯄꯨꯝꯅꯃꯛꯇ (n + 1) ꯁꯨꯕꯥ ꯐꯤꯕꯣꯅꯥꯆꯤ ꯃꯁꯤꯡ ꯍꯥꯄꯆꯤꯜꯂꯒꯥ 1 ꯀꯥꯟꯅꯕ ꯊꯃꯖꯤꯜꯂꯤꯕꯅꯣ?
ꯄꯥꯎꯈꯨꯝ ꯎꯠꯄ
ꯄꯥꯎꯈꯨꯝ ꯃꯥꯏꯊꯤꯕ n ꯄꯨꯟꯁꯤꯜꯂꯕꯗ (n + 2) ꯁꯨꯕꯥ ꯐꯤꯕꯣꯅꯥꯆꯤ ꯃꯁꯤꯡꯗꯒꯤ 1 ꯂꯧꯊꯣꯀꯄ ꯑꯣꯏ, ꯑꯃꯁꯨꯡ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯅꯤ ꯑꯗꯨ ꯃꯊꯪꯒꯤ ꯃꯁꯤꯡ ꯑꯅꯤꯅꯤ, ꯃꯈꯣꯌ ꯄꯨꯟꯅ ꯃꯗꯨꯗꯒꯤ (n + 1) ꯁꯨꯕꯥ ꯃꯁꯤꯡ ꯍꯥꯄꯆꯤꯜꯂꯒꯥ 1 ꯍꯦꯟꯅꯥ ꯆꯥꯎꯏ꯫
1, 1, 2, 3, 5 … ꯒꯤꯗꯃꯛ F₁, F₂, F₃ … ꯏꯕꯤꯌꯨ꯫ ꯃꯁꯤꯡ ꯈꯨꯗꯤꯡꯃꯛ ꯃꯃꯥꯡꯗ ꯂꯩꯕ ꯑꯅꯤꯒꯤ ꯄꯨꯟꯁꯤꯟꯕꯅꯤ꯫
ꯃꯥꯏꯊꯤꯕꯁꯤꯡ: F₁ + F₂ + … + Fₙ꯫ ꯄꯨꯟꯁꯤꯟꯕ ꯑꯗꯨꯗ 1 ꯍꯥꯄꯆꯤꯟꯕꯤꯌꯨ, F₂ ꯑꯣꯏꯅ ꯏꯗꯨꯅ, ꯑꯃꯁꯨꯡ ꯃꯗꯨ ꯄꯨꯟꯁꯤꯟꯗꯨꯅ ꯆꯠꯂꯤ: F₂ + F₁ = F₃, ꯃꯗꯨꯒꯤ ꯃꯇꯨꯡꯗ F₃ + F₂ = F₄, ꯑꯁꯤꯅꯆꯤꯡꯕ, ꯄꯨꯟꯁꯤꯟꯕ ꯄꯨꯝꯅꯃꯛ Fₙ₊₂ ꯑꯣꯏꯕ ꯐꯥꯑꯣꯕ꯫ ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯥꯏꯊꯤꯕꯁꯤꯡꯒꯤ ꯄꯨꯝꯅꯃꯛ Fₙ₊₂ − 1 ꯅꯤ꯫
ꯃꯥꯏꯄꯥꯛꯄꯁꯤꯡ ꯑꯗꯨ ꯃꯊꯪꯒꯤ ꯊꯝꯂꯕ ꯁꯦꯜ ꯑꯅꯤꯅꯤ, Fₙ₊₁ ꯑꯃꯁꯨꯡ Fₙ₊₂꯫ ꯀꯥꯟꯅꯕ ꯁꯦꯜ: Fₙ₊₁ + Fₙ₊₂ − (Fₙ₊₂ − 1) = Fₙ₊₁ + 1꯫ ꯃꯥꯏꯊꯤꯕ ꯃꯔꯤꯗ, ꯃꯗꯨ F₅ + 1 = ꯌꯨꯅꯤꯠ 6 ꯅꯤ꯫

ꯅꯣꯛꯅꯕꯒꯤ ꯀꯃꯤꯛ

ꯒꯣꯜꯗꯦꯟ ꯔꯦꯁꯤꯑꯣꯅ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯋꯥꯡꯕ ꯕꯦꯠꯀꯤ ꯈꯣꯟꯖꯦꯜ ꯎꯅꯈꯤ꯫

ꯍꯧꯔꯛꯐꯃꯁꯤꯡ

RouletteDoc꯫ ꯊꯧꯔꯥꯡꯒꯤ ꯃꯔꯣꯜ ꯑꯃꯁꯨꯡ ꯈꯨꯗꯃꯁꯤꯡ꯫ https://roulettedoc.com/strategy/fibonacci
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Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010꯫ ꯆꯦꯞꯇꯔ 13, ꯔꯨꯂꯦꯠ꯫
Epstein, R. A. The Theory of Gambling and Statistical Logic, 2nd ed. Academic Press, 2013.
Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette. CRC Press, 2021꯫ ꯆꯦꯞꯇꯔ 2, ꯔꯨꯂꯦꯠ꯫
Sigler, L. E. Fibonacci’s Liber Abaci: A Translation into Modern English of Leonardo Pisano’s Book of Calculation. Springer, 2002꯫ ꯆꯦꯞꯇꯔ 12, ꯂꯝꯍꯥꯎꯒꯤ ꯁꯃꯁ꯭ꯌꯥ꯫
Singh, P. The so-called Fibonacci numbers in ancient and medieval India. Historia Mathematica 12 (3), 1985, pp. 229–244.

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