A pie 16

A pie is divided into 100 guests. Guest 1 gets 1%, guest 2 gets 2% of what left,... and so on. Who gets the largest piece of pie?

Correct answer:

n = 10

Step-by-step explanation:

r_{1} = 1 % = \frac{1}{1 0 0} = 0.01 z_{1} = 1 r_{2} = 0.02 \cdot z_{1} = 0.02 \cdot 1 = \frac{1}{5 0} = 0.02 z_{2} = z_{1} - r_{2} = 1 - 0.02 = \frac{4 9}{5 0} = 0.98 r_{3} = 0.03 \cdot z_{2} = 0.03 \cdot 0.98 = \frac{1 4 7}{5 0 0 0} = 0.0294 z_{3} = z_{2} - r_{3} = 0.98 - 0.0294 = 0.9506 r_{4} = 0.04 \cdot z_{3} = 0.04 \cdot 0.9506 ≐ 0.038 z_{4} = z_{3} - r_{4} = 0.9506 - 0.038 ≐ 0.9126 r_{5} = 0.05 \cdot z_{4} = 0.05 \cdot 0.9126 ≐ 0.0456 z_{5} = z_{4} - r_{5} = 0.9126 - 0.0456 ≐ 0.8669 r_{6} = 0.06 \cdot z_{5} = 0.06 \cdot 0.8669 ≐ 0.052 z_{6} = z_{5} - r_{6} = 0.8669 - 0.052 ≐ 0.8149 r_{7} = 0.07 \cdot z_{6} = 0.07 \cdot 0.8149 ≐ 0.057 z_{7} = z_{6} - r_{7} = 0.8149 - 0.057 ≐ 0.7579 r_{8} = 0.08 \cdot z_{7} = 0.08 \cdot 0.7579 ≐ 0.0606 z_{8} = z_{7} - r_{8} = 0.7579 - 0.0606 ≐ 0.6973 r_{9} = 0.09 \cdot z_{8} = 0.09 \cdot 0.6973 ≐ 0.0628 z_{9} = z_{8} - r_{9} = 0.6973 - 0.0628 ≐ 0.6345 r_{10} = 0.1 \cdot z_{9} = 0.1 \cdot 0.6345 ≐ 0.0635 z_{10} = z_{9} - r_{10} = 0.6345 - 0.0635 ≐ 0.5711 r_{11} = 0.11 \cdot z_{10} = 0.11 \cdot 0.5711 ≐ 0.0628 z_{11} = z_{10} - r_{11} = 0.5711 - 0.0628 ≐ 0.5082 r_{12} = 0.12 \cdot z_{11} = 0.12 \cdot 0.5082 ≐ 0.061 z_{12} = z_{11} - r_{12} = 0.5082 - 0.061 ≐ 0.4472 r_{13} = 0.13 \cdot z_{12} = 0.13 \cdot 0.4472 ≐ 0.0581 z_{13} = z_{12} - r_{13} = 0.4472 - 0.0581 ≐ 0.3891 r_{14} = 0.14 \cdot z_{13} = 0.14 \cdot 0.3891 ≐ 0.0545 z_{14} = z_{13} - r_{14} = 0.3891 - 0.0545 ≐ 0.3346 r_{15} = 0.15 \cdot z_{14} = 0.15 \cdot 0.3346 ≐ 0.0502 z_{15} = z_{14} - r_{15} = 0.3346 - 0.0502 ≐ 0.2844 r_{16} = 0.16 \cdot z_{15} = 0.16 \cdot 0.2844 ≐ 0.0455 \dots max r_{i} = r_{10} = 0.0635 n = 10

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