For the series

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

Problem

For the series ∑n=1∞1n2\displaystyle\sum_{n=1}^{\infty}\frac{1}{n^{2}}, one finds that lim⁡n→∞1n2=0\displaystyle \lim_{n\to\infty}\frac{1}{n^{2}}=0. Which statement is justified solely by knowing this limit? (a) The series converges because its terms approach 00. (b) The series diverges because, for a pp-series with p>1p>1, the test guarantees divergence. (c) No conclusion about convergence can be drawn from this limit alone. (d) The series oscillates because its terms alternate in sign.

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