Question

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

Answer 1

Sum of n Natural Numbers = $\frac {n(n+1)}{2}$

Step-by-step explanation:

Given,  

The nth term is ($\frac {n}{x} + y$)

We know that,

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

So, Sum of r terms = $\sum (\frac {n}{x} + y)_{n=1}^{r}$

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

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

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

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

Since sum of n natural numbers = $\frac {n(n+1)}{2}$