Mathematics

Mathematics

Problem

Let P=∑k=251k(ln⁡k)2P=\displaystyle\sum_{k=2}^{5}\frac{1}{k(\ln k)^2} be the sum of the first four nonzero terms of the series S=∑k=2∞1k(ln⁡k)2\displaystyle S=\sum_{k=2}^{\infty}\frac{1}{k(\ln k)^2}. Which interval must contain SS? a) 1.96<S<2.021.96 < S < 2.02 b) 2.22<S<2.292.22 < S < 2.29 c) 2.08<S<2.152.08 < S < 2.15 d) 2.14<S<2.202.14 < S < 2.20

Browse the problem library