Prove that

\( \sum_{r=1}^n rr! = (n+1)!-1 \)

for \( n>1\)

In order to prove a mathematical identity, one needs to show that the identity is valid for all the values in the desired range. Trying all the values in that range is practically impossible.

The induction method starts by proving the identity for the smallest value in the range, n=1 in this case.

It then assumes that the identity is true for another value, usually taken as n=k. Based on that assumption, it proves that the identity is true for the next value, n=k+1.

Given the identity is true for n=1, this shows it is also true for n=2, which shows it is true for n=3 and so on…

The steps to follow for a proof by induction are:

1) Prove for n=1

2) Assume true for n=k

3) Prove for n=k+1

Below you can find my solution for the question above