Question Number 134484 by mohammad17 last updated on 04/Mar/21
![](https://www.tinkutara.com/question/19212.png)
Commented by Dwaipayan Shikari last updated on 04/Mar/21
![General term=(n/(n^2 −(n−1)^2 ))=(n/(2n−1)) lim_(n→∞) (n/(2n−1))=(1/2) (Sequence converges to (1/2)) And the series is Divergent Σ_(n=1) ^∞ (n/(2n−1))→∞](https://www.tinkutara.com/question/Q134491.png)
$${General}\:{term}=\frac{{n}}{{n}^{\mathrm{2}} −\left({n}−\mathrm{1}\right)^{\mathrm{2}} }=\frac{{n}}{\mathrm{2}{n}−\mathrm{1}} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{{n}}{\mathrm{2}{n}−\mathrm{1}}=\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\left({Sequence}\:{converges}\:{to}\:\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$$${And}\:{the}\:{series}\:{is}\:{Divergent}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}}{\mathrm{2}{n}−\mathrm{1}}\rightarrow\infty \\ $$