How would I show this: If the series a_n with a_n > 0 is convergent, and if b_n = (a1 + a2 + .... + an)/n for n in N, then show that the series b_n is always divergent. Thanks for your help.
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Originally Posted by jamesHADDY How would I show this: If the series a_n with a_n > 0 is convergent, and if b_n = (a1 + a2 + .... + an)/n for n in N, then show that the series b_n is always divergent. Thanks for your help. $\displaystyle b_n = \frac{a_1+\cdots+a_n}{n} \geq \frac{a_1}{n} $. But, $\displaystyle \sum_{n=1}^{\infty} \frac{a_1}{n} = \infty$.
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