(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Is the 50th partial sum, s_50, of the alternating series, "summation [(-1)^(n-1)] / n from 1-->infinity" an overestimate or an underestimate of the total sum? Explain

3. The attempt at a solution

First concern: Isn't every partial sum an underestimate for an increasing sequence and an overestimate for a decreasing sequence?

Secondly, I saw that b_n = 1/n, which is a divergent sum. So since it is increasing and divergent, wouldn't the partial sum s_50 be an underestimate?

This seems to be too easy a conclusion, so does anyone know if there is any other way to justify it?

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# Sum of a series problem

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