Consider the series $∑_{n=1}^∞ x^2+ n/n^2$ . Pick out the true statements:

Consider the series
$\sum_{n=1}^\infty x^2+ n/n^2$
.
Pick out the true statements:
(a) The series converges for all real values of $x$.
(b) The series converges uniformly on $\mathbb{R}$.
(c) The series does not converge absolutely for any real value of $x$.

Solutions Collecting From Web of "Consider the series $∑_{n=1}^∞ x^2+ n/n^2$ . Pick out the true statements:"
Hint: $$\sum_{n=1}^\infty\frac{1}{n}=\sum_{n=1}^\infty\frac{n}{n^2}\leq\sum_{n=1}^\infty x^2+\frac{n}{n^2}.$$
If you inadvertently meant $(x^2+n)/n^2$, then $$\sum_{n=1}^\infty\frac{1}{n}=\sum_{n=1}^\infty\frac{n}{n^2}\leq\sum_{n=1}^\infty\frac{x^2+n}{n^2}.$$
Only (c) applies. because $\sum_{n\ge 1} {1/n}$ diverges..