Functions and functions!

Calculus Level 4

In=0π4tannxdx\large I_{n} = \int_{0}^{\frac{\pi}{4}} \tan ^{n}x \, dx

We define the integral as above. And define the relation f(n)=1In2In+2 f(n) = \dfrac{1}{I_{n-2} - I_{n+2}} . Evaluate the summation below.

2r=210f(r) \large 2\sum_{r=2}^{10} f(r)

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