Let fn = ∫ ; x ∈ (0,π/2) (∑ sin^k-1 x ; x ∈ (k=1,n)) (∑ (2k-1) sin^k-1 x ; x ∈ (k=1,n)) cosx dx, n ∈ N. Then f21 – f20 is equal to____.

Question

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

Answer 1

Correct answer is 41