Let f(x) be a real differentiable convex function with f'(x)tend to 0 as x goes to infinity.prove that the limit as n goes to infinity of (0.5f(1)+f(2)+f(3)+...f(n-1)+f(n)-(integral of f(x) from 1 to n)) is final and positive.

Convex function

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hedipaldi

Let f(x) be a real differentiable convex function with f'(x)tend to 0 as x goes to infinity.prove that the limit as n goes to infinity of (0.5f(1)+f(2)+f(3)+...f(n-1)+f(n)-(integral of f(x) from 1 to n)) is final and positive.

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