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f-fonction-numerical-increasing-on-0-1-and-0-1-f-t-dt-converges-prove-that-lim-n-gt-1-n-k-1-n-f-k-n-0-1-f-t-dt-

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Question Number 27601 by abdo imad last updated on 10/Jan/18
f fonction numerical increasing on ]0,1] and ∫_0 ^1 f(t)dt converges prove that lim_(n−>∝) (1/n) Σ_(k=1) ^n f((k/n)) = ∫_0 ^1 f(t)dt .
ffonctionnumericalincreasingon]0,1]and∫01f(t)dtconvergesprovethatlimn−>∝1n∑k=1nf(kn)=∫01f(t)dt.

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