Sum to infinity formula proof

1. How do you derive sum to infinity?
2. What is the sum of N to infinity?

How do you derive sum to infinity?

The proof of the sum to infinity formula is derived from the formula for the first n terms of a geometric series: S_n=a[1-rⁿ]/[1-r]. If -1<r<1 then as n→∞, rⁿ→0.

What is the sum of N to infinity?

The answer is n(n+1)/2. Atleast, this is what we were taught all throughout our schooling. So, if 'n' were to tend to infinity, summation should tend to infinity.