# Math Help - limits

1. ## limits

how do you find-

$\lim_{x\to \infty}(\frac{1}{a+n}+\frac{1}{2a+n}+\frac{1}{3a+n}+.....+\frac{1}{an+n})$

2. Originally Posted by adhyeta
how do you find-

$\lim_{x\to \infty}(\frac{1}{a+n}+\frac{1}{2a+n}+\frac{1}{3a+n}+.....+\frac{1}{an+n})$
Limits is not my strongest suit, but how can this be found for x approaches infinity if the function in question is not a function of x?

3. Originally Posted by pickslides
Limits is not my strongest suit, but how can this be found for x approaches infinity if the function in question is not a function of x?
oops. its actually n not x. lol. thnx

4. Originally Posted by adhyeta
how do you find-

$\lim_{x\to \infty}(\frac{1}{a+n}+\frac{1}{2a+n}+\frac{1}{3a+n}+.....+\frac{1}{an+n})$

This can be identified with a Reimann sum

$\lim_{n \to \infty}\sum_{i=1}^{n}\frac{1}{i\cdot a+n} = \sum_{i=1}^{n}\frac{1}{1+\frac{i\cdot a}{n}}\left( \frac{1}{n}\right)=\int_{0}^{a}\frac{1}{1+x}dx=\ln |a+1|$