# trying to proove this limit equality to a specific integral [closed]

can you help me prove this equality?

I tried to use Riemann sums but I haven't succeeded to find something useful.

$$\lim_{n\to\infty} \sum_{k=1}^n f\left(\frac{k}{n}\right)\frac{1}{n} = \int_0^1f(x)dx$$

Thank you very much.

## closed as off-topic by RRL, NCh, Eevee Trainer, Adrian Keister, LeucippusApr 6 at 4:01

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• What did you get with Riemann sums? Also, summing from $n=1$ to $n$ doesn't make sense – J. W. Tanner Apr 2 at 17:02
• This is an immediate consequence of the definition of Riemann integral. Here the partition is uniform with points $x_k=k/n$ and tags $t_k$ are choosen the same as $x_k$ so the Riemann sum becomes $\sum_{k=1}^{n}f(t_k)(x_k-x_{k-1})$. – Paramanand Singh Apr 3 at 17:24