Question

A series whose $n^{th}$ term is $⟮\frac{n}{x}⟯+y$, the sum of r terms will be

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

Answer 1

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

$a_n=\frac{n}{x}+y$

Sum of r terms

$={\sum }_{n=1}^r(\frac{n}{x}+y)$

$={\sum }_{n=1}^r\frac{n}{x}+{\sum }_{n=1}^{r}y$

$=(\frac{1}{x}+\frac{2}{x}+.........+\frac{r}{x})+(y+y+.........+y)$

$=\frac{1}{x}(1+2+3+...........+r)+ry$

$=\frac{r(r+1)}{2x}+ry$