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Miklós Schweitzer 2007 Problem 8

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March 3, 2017
Miklos Schweitzerreal analysiscollege contests

Problem Statement

For an A={ai}i=0∞A=\{ a_i\}^{\infty}_{i=0} sequence let SA={a0,a0+a1,a0+a1+a2,…}SA=\{ a_0, a_0+a_1, a_0+a_1+a_2, \ldots\} be the sequence of partial sums of the a0+a1+…a_0+a_1+\ldots series. Does there exist a non-identically zero sequence AA such that all of the sequences A,SA,SSA,SSSA,…A, SA, SSA, SSSA, \ldots are convergent?
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