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Find the period of tan(x+4x+9x+.......+...

Find the period of `tan(x+4x+9x+.......+n^2x)` (n any positive integer)

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Suppose that f: R to R is a continuous periodic function and T is the period of it . Let a in R . Then prove that for any positive integer n int_(0)^(a+nT) f(x)dx=n int_(a)^(a+T) f(x) dx