# Summation of integrals!

Calculus Level pending

For $$a_{k} =\displaystyle \int_{0}^{\frac{\pi}{2}} \sin 2x {(1 - \sin x)}^{\frac{k-1}{2}} \text{dx}$$,

$$\displaystyle \sum_{k=3}^{\infty} (k+1)(a_{k} - a_{k+1})$$ can be expressed as $$\frac{a}{b}$$, where $$a$$, and $$b$$ are coprime, then find $$a \times b$$.

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