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Definite Integration question

2024 · 6 Apr · Shift 1 · Q58

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JEE Main
Mathematics
Definite Integration
2024 · 6 Apr · Shift 1 · Q58

Definite Integration question

2024 · 6 Apr · Shift 1 · Q58

JEE MainMathematicsDefinite IntegrationNumerical+4 / −1

Let

r_k=\frac{\int_0^1\left(1-x^7\right)^k d x}{\int_0^1\left(1-x^7\right)^{k+1} d x}, k \in \mathbb{N}

. Then the value of

\sum_{k=1}^{10} \frac{1}{7\left(r_k-1\right)}

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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