Suppose we have a postiive, differentiable function such that |f'(x)| <= f(x) for any x. Prove that the integral from of converges iff the sum from of f(n) converges
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Sorry I should have added that a hint was to use legrange to show that for every , and every in [n,n+1], f(n)/10 <= f(x) <= 10f(n) Or perhaps an easier way to solve it?
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