I'm currently reading a book in which part of the solution to the problem involve this identity:
$$\sum_{j=i+1}^{n}j = \sum_{j=1}^{n}j-\sum_{j=1}^{i}j$$
Which I cannot derive myself. The only thing I can do with it is this:
$$\sum_{j=i+1}^{n}j = \sum_{j=1}^{n}j+i = \sum_{j=1}^{n}j + \sum_{j=1}^{i}i$$
Which seems to me completely useless.
Any help in understanding this (as I am unaccustomed to summation manipulation in general) would be greatly appreciated.
I know it's related to " Calculate integer summation when lower bound is a variable " but I still don't see the why.