# Limit is Sum

#### jeffer vitola

##### New member
hello ........... I propose this exercise for you to solve on various methods .......

$\lim_{n \to{+}\infty}{\frac{1}{n}\sum_{i=1}^n({1+\frac{i}{n}}})^{-2}$

thanks

att
jefferson alexander vitola

#### MarkFL

Staff member
I have moved this topic, as it seems to be posted as a challenge rather than for help.

#### ZaidAlyafey

##### Well-known member
MHB Math Helper
$\lim_{n \to{+}\infty}{\frac{1}{n}\sum_{i=1}^n({1+\frac{i}{n}}})^{-2}$
This can be solved directly using the Riemann sum

$$\displaystyle \lim_{n \to{+}\infty} \sum_{i=1}^n \frac{n}{(n+i)^2}=\int^2_1 \frac{1}{x^2}\, dx = \frac{1}{2}$$

#### jeffer vitola

##### New member
This can be solved directly using the Riemann sum

$$\displaystyle \lim_{n \to{+}\infty} \sum_{i=1}^n \frac{n}{(n+i)^2}=\int^2_1 \frac{1}{x^2}\, dx = \frac{1}{2}$$
hello........interesting, but as I said in my previous forum topic or main focus is that you develop by various methods ...... one can be evaluated by the summation properties and then calculate its limit for example,,,,,,,, if you are cant make exercise , there is not problem,,,, thanks........

att
jefferson alexander vitola