KVPY #20

Calculus Level 4

If In=0π/4tannx dx I_{n} = \displaystyle\int_{0}^{π/4} \tan^{n} x \ dx , then 1I2+I4 \dfrac{1}{I_{2} + I_{4}} , 1I3+I5 \dfrac{1}{I_{3} + I_{5}} , 1I4+I6 \dfrac{1}{I_{4} + I_{6}} follows a/an __________\text{\_\_\_\_\_\_\_\_\_\_} in that order.


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