MathDB
2016 Guts #13

Source:

August 14, 2022
2016Guts Round

Problem Statement

Suppose {an}n=1∞\{a_n\}_{n=1}^\infty is a sequence. The partial sums {sn}n=1∞\{s_n\}_{n=1}^\infty are defined by sn=∑i=1nai.s_n=\sum_{i=1}^na_i. The Cesàro sums are then defined as {An}n=1∞\{A_n\}_{n=1}^\infty, where An=1n⋅∑i=1nsi.A_n=\frac{1}{n}\cdot\sum_{i=1}^ns_i. Let an=(−1)n+1a_n=(-1)^{n+1}. What is the limit of the Cesàro sums of {an}n=1∞\{a_n\}_{n=1}^\infty as nn goes to infinity?
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