Suppose that a series $\sum a_{n}$ has positive terms and its partial sums $s_{n}$ satisfy the inequality $s_{n} \leqslant 1000$ for all $n .$ Explain why $\Sigma a_{n}$ must be convergent.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.4: Series And Their Notations
Problem 1SE: What is an nth partial sum?
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Suppose that a series $\sum a_{n}$ has positive terms and its partial sums $s_{n}$ satisfy the inequality $s_{n} \leqslant 1000$ for all $n .$ Explain why $\Sigma a_{n}$ must be convergent.

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