Comparison Tests

Limit Convergence Test

The ratio between $\frac{n+1}{2n^2}$ and $\frac{1}{n}$ for $n \rightarrow ∞$ is $\frac{1}{2}$. Since the sum of the sequence $\frac{1}{n}$ $\left ( \text{i.e., }\sum {\frac{1}{n}}\right)$ diverges, the limit convergence test tells that the original series (with $\frac{n+1}{2n^2}$) also diverges.

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Comparison Tests

Limit Convergence Test

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