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Sequence

Source: Iran 2005

August 27, 2005
limitalgebra proposedalgebra

Problem Statement

Suppose {xn}\{x_n\} is a decreasing sequence that lim⁡n→∞xn=0\displaystyle\lim_{n \rightarrow\infty}x_n=0. Prove that ∑(−1)nxn\sum(-1)^nx_n is convergent
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