# Which-one-of-the-following-series-is-Not-convergent-A-r-1-1-r-3-B-r-1-1-r-2-C-r-1-1-r-2-4-D-r-1-1-5r-

Question Number 76815 by Rio Michael last updated on 30/Dec/19
$$\mathrm{Which}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{series}\:\mathrm{is}\:\boldsymbol{\mathrm{N}}\mathrm{o}\boldsymbol{\mathrm{t}}\:\mathrm{convergent}? \\$$$$\mathrm{A}.\:\underset{\mathrm{r}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{r}^{\mathrm{3}} } \\$$$$\mathrm{B}.\:\underset{\mathrm{r}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{r}^{\mathrm{2}} } \\$$$$\mathrm{C}.\:\underset{\mathrm{r}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{r}^{\mathrm{2}} −\mathrm{4}} \\$$$$\mathrm{D}.\:\underset{\mathrm{r}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{5r}} \\$$
Commented by JDamian last updated on 30/Dec/19
$${D} \\$$
Commented by Rio Michael last updated on 30/Dec/19
$$\mathrm{thank}\:\mathrm{you} \\$$
Answered by 21042004 last updated on 01/Jan/20
$$\mathrm{C}. \\$$$$\mathrm{If}\:\mathrm{r}=\mathrm{2},\:\mathrm{then}\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} −\mathrm{4}}=\frac{\mathrm{1}}{\mathrm{0}} \\$$