# Proof : Sequence of Partial Sums

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Suppose a_k is a nonincreasing sequence satisfying a_k --> 0 as k--> infinity. Also suppose the sequence of partial sums by s_n = l summation k = 1 to n of b_kl is bounded.

Show that these conditions imply summation k = 1 to n of a_k*b_k is convergent.

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A sequence of partial sums proof is provided. The solution is detailed and well presented.

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Suppose a_k is a nonincreasing sequence satisfying a_k --> 0 as k--> infinity. Also suppose the sequence of partial sums by s_n = l summation k = 1 to n of b_kl is bounded.

Show that these conditions imply summation k = 1 to n of a_k*b_k is convergent.

Solution:

The ordered pair of ...

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