Question

A series whose nth term is (n/x)+y,then sum of r terms will be ​

Answer 1

The required sum is $\dfrac{r(r+1)}{2x} + ry$.

Step-by-step explanation:

• Since, we are given the $n^t^h$ term as;

• So, $T_n = \dfrac{n}{x} + y$

We can apply the summation operator to find out the sum of r terms.

We apply as;

• Sum of r terms =$\sum_{n=1}^{r}\left ( \dfrac{n}{x}+y \right )$

= $\sum_{n=1}^{r}\left ( \dfrac{n}{x} \right ) + \sum_{n=1}^{r}y$

= $\left ( \dfrac{1}{x}+\dfrac{2}{x}+..r \ terms...+\dfrac{r}{x} \right ) + (y+y+.....r \ terms.....+y)$

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

= $\dfrac{1}{x} \times \dfrac{r(r+1)}{2} + ry$ (This is the required sum)

Thus, the required sum is $\dfrac{r(r+1)}{2x} + ry.$