Question

Let fn = $\int\limits_0^{\pi/2}$ $\left(\displaystyle\sum_{k=1}^{n}\,sin^{k-1}x\right)\left(\displaystyle\sum_{k=1}^{n}\,(2k-1)sin^{k-1}x\right)$ cosx dx, n ∈ N. Then f21 – f20 is equal to____.

Answer 1

The correct answer is 41.