Find the sum `Sigma_(r=1)^(n) r/((r+1)!)`. Also, find the sum of infinite terms.

Explanation

To solve the problem of finding the sum \( S = \sum_{r=1}^{n} \frac{r}{(r+1)!} \) and the sum of infinite terms, we can follow these steps:

### Step 1: Rewrite the term
We start with the term \( \frac{r}{(r+1)!} \). We can rewrite \( r \) as \( (r+1) - 1 \):
\[ \frac{r}{(r+1)!} = \frac{(r+1) - 1}{(r+1)!} = \frac{r+1}{(r+1)!} - \frac{1}{(r+1)!} \]
This simplifies to:
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