Let r_k = _0^1(1 - x^7)^kdx _0^1(1 - x^7)^ k+1 dx , k ∈ N. Then the value of _ k=1 ^ 10 1 7(r_k - 1) is equal...

Question

Let r_k = _0^1(1 - x^7)^kdx _0^1(1 - x^7)^ k+1 dx , k ∈ N. Then the value of _ k=1 ^ 10 1 7(r_k - 1) is equal to _____.

Accepted Answer

65

JEE Main 2024 Mathematics question