Explanation:

The series is in the form n(n + 1)² = n³ + 2n² + n
Then Σ n³ + 2n² + n = [n/(n+1)2 ]² + 2 [n (n + 1)2n+1)/6] + [n/(n+1)2]
Substituting n = 10 will give the sum of the series. Thus Σ [10∗11)/2]² + [10∗11∗21)/6 ] + [10∗11)/2]
= 3850