Question
Proof Suppose that $\Sigma a_{n}$ and $\Sigma b_{n}$ are series with positive terms. Prove that if$\lim _{n \rightarrow \infty} \frac{a_{n}}{b_{n}}=\infty$and $\Sigma b_{n}$ diverges, then $\Sigma a_{n}$ also diverges.
Step 1
This is because the limit of the ratio of $a_n$ and $b_n$ as $n$ approaches infinity is infinity, which means that after a certain point, the ratio of $a_n$ to $b_n$ is always greater than 1. Show more…
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