Consider the tail

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Consider the tail RN=∑n=N+1∞1n2R_N=\displaystyle\sum_{n=N+1}^{\infty}\frac1{n^{2}}, where NN is a positive integer. Which of the following values of NN is the smallest that guarantees RN<0.0005R_N<0.0005? (a) 20002000 (b) 25002500 (c) 20012001 (d) 19991999

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