Mathematics

Problem

Let

S_n

be the area of the figure enclosed by a curve

y = x^2(1-x)^n

(

0 \le x \le 1

) and x-axis, if

\lim_{n \to \infty} \sum_{k=1}^{n} S_k = \frac{1}{\sqrt{A}}, \text{ then 'A' is equal to}