1.

(i) If f_(n)(x)=(n+1)/((n-1)!)x^(n), then find the value of int_(0)^(1)[sum_(n=1)^(oo)f_(n)(x)]dx. (ii) Evaluate int_(0)^(2)lim_(nrarroo)int_(r=0)^(n)(x^(r+1))/(r!)5^(r)dx.

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