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HKIMO 2026 THPT (Grades 10–12 shared) National Final (Heat) Set 05 Question 13

HKIMO · HKIMO 2026 THPT (Grades 10–12 shared) National Final (Heat) Set 05

Question 13

Given $\log 2=0.301$, evaluate $\displaystyle\log\left(\sum_{n=0}^{2015}\binom{2015}{n}\right)$ to two decimal places.

Editorial working convention: Use the supplied approximation and ordinary half-up rounding.