Question: Let be a positive, continuous, and decreasing function for x 1, such that a n = (n). Prove that if the series converges

Let ƒ be a positive, continuous, and decreasing
function for x ≥ 1, such that an = ƒ(n). Prove that if the series

n=1

converges to S, then the remainder RN S - SN is bounded by

n=1

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