Question

A series, whose $n^{th}$ term is $\left(\frac{n}{x}\right)+y$, then sum of $r$ terms will be :

• A. $\left\{\frac{r(r+1)}{2x}\right\}+ry$
• B. $\left\{\frac{r(r-1)}{2x}\right\}$
• C. ${\left\{\frac{r(r-1)}{2x}\right\}}^2-xy$
• D. $\left\{\frac{r(r+1)}{2x}\right\}-rx$

Answer 1

The correct option is A $\left\{\frac{r(r+1)}{2x}\right\}+ry$

Let $T_n=\left(\frac{n}{x}\right)+y$
$S_r=\frac{1}{x}\sum _1^{r}n+y\sum _1^{r}1$
$\Rightarrow S_n=\{\frac{r(r+1)}{2x}+ry\}$