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)) = ∫


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Question Number 27601 by abdo imad last updated on 10/Jan/18

$f f o n c t i o n n u m e r i c a l i n c r e a s i n g o n] 0, 1] a n d$ $\int_{0}^{1} f (t) d t c o n v e r g e s p r o v e t h a t {l i m}_{n - >\propto} \frac{1}{n} \sum_{k = 1}^{n} f (\frac{k}{n})$ $= \int_{0}^{1} f (t) d t .$
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