Continuing from the previous post on this subject, lets find the formulas for the sum of the two series I mentioned in the previous post, the arithmetic and the geometric progressions:
Firstly, lets look on a very simple case - the progression 1+2+3+...+n=S. If we just look on it, it is not very clear what the sum is. However, if we will write it in a slightly different manner the answer will be obvious:
Now lets look on the general case. The general arithmetic series is:
By the way, this formula requires to know the first number in the progression. However, if you know the last one instead of the first you can also use this formula - after changing d to (-d).
Firstly, lets again consider a specific case. Lets look on the sum of the following progression: