Sum the series : `x(x+y)+x^2(x^2+y^2)+x^3(x^3+y^3+ ton` terms.

Explanation

To sum the series \( S_n = x(x+y) + x^2(x^2+y^2) + x^3(x^3+y^3) + \ldots \) up to \( n \) terms, we can break it down step by step.

### Step-by-Step Solution:

1. **Identify the General Term**:
The general term of the series can be expressed as \( T_k = x^k (x^k + y^k) \) for \( k = 1, 2, \ldots, n \). This can be rewritten as:
\[
T_k = x^{2k} + x^k y^k
...