3

I have doubts how to solve summation if on the top there is something else than $n$ more specificially:

$$\sum\limits_{i=1}^{n+1} i=\frac{(n+1)(n+2)}{2}$$

Is my solution correct? I just replace $n+1$ to $n$ in the formula for the special case of arithmetic series.

ocram
  • 743
  • 2
  • 7
  • 15

1 Answers1

4

Write $k=n+1$ then the sum becomes: $$\sum\limits_{i=1}^{k} i=\frac{k(k+1)}{2},$$ you can prove it using the induction. Now substitute $k$ with $n+1$ and you obtain the result.

InsideOut
  • 6,883