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For a natural number n, let an = int0^(p...

For a natural number n, let `a_n = int_0^(pi/4) (tanx)^(2n) dx`. Now answer the following questions. Express (1) `a_(n+1)` in terms of `a_n` (2) Find `lim_(n->oo) a_n` (3) Find `lim_(n->oo) sum_(k=1)^n (-1)^(k-1) (a_k+a_(k-1))`

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