KVPY #20

Calculus Level 4

If \( I_{n} = \displaystyle\int_{0}^{π/4} \tan^{n} x \ dx \), then \( \dfrac{1}{I_{2} + I_{4}} \), \( \dfrac{1}{I_{3} + I_{5}} \), \( \dfrac{1}{I_{4} + I_{6}}\) follows a/an \(\text{__________} \) in that order.

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