Find the sum `Sigma_(r=1)^(n) 1/(r(r+1)(r+2)(r+3))`
Also,find `Sigma_(r=1)^(oo) 1/(r(r+1)(r+2)(r+3))`

Explanation

To find the sum \( S_n = \sum_{r=1}^{n} \frac{1}{r(r+1)(r+2)(r+3)} \) and also \( S_\infty = \sum_{r=1}^{\infty} \frac{1}{r(r+1)(r+2)(r+3)} \), we can follow these steps:

### Step 1: Simplify the term
We start with the term \( \frac{1}{r(r+1)(r+2)(r+3)} \). We can use partial fraction decomposition to rewrite this term.

Assume:
\[
\frac{1}{r(r+1)(r+2)(r+3)} = \frac{A}{r} + \frac{B}{r+1} + \frac{C}{r+2} + \frac{D}{r+3}
...