Question
Prove the following extension of the Limit Comparison Test: if $\lim _{k \rightarrow \infty} \frac{a_{k}}{b_{k}}=0$ and $\sum_{k=1}^{\infty} b_{k}$ converges, then $\sum_{k=1}^{\infty} a_{k}$ converges.
Step 1
This implies that there exists some $N_0$ such that for all $k > N_0$, $|a_k| < |b_k|$. Show more…
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