determine if they are converge

**wopashui** · March 21st 2010, 09:48 AM

$\sqrt{n+1}/2\sqrt{n}$

$(1+1/n)^{2n}$

$2^n/n^2$

$sin n / \sqrt{n}$

$\sqrt {n^2+n} - n$

can anyone tell me the general methods for simplfing these sequence so it looks more obvious?

**running-gag** · March 21st 2010, 09:56 AM

Hi

$\sqrt {n^2+n} - n = \frac{\left(\sqrt {n^2+n} - n\right)\left(\sqrt {n^2+n} + n\right)}{\sqrt {n^2+n} + n}$

$\sqrt {n^2+n} - n = \frac{n}{\sqrt {n^2+n} + n}$

$\sqrt {n^2+n} - n = \frac{1}{\sqrt {1+\frac{1}{n}} + 1}$

**General** · March 21st 2010, 10:52 AM

Originally Posted by wopashui

$\sqrt{n+1}/2\sqrt{n}$

$\color{red}=\frac{1}{2}\sqrt{\frac{n+1}{n}}=\frac{ 1}{2}\sqrt{1+\frac{1}{n}}$

$(1+1/n)^{2n}$

$\color{red} \left(1+\frac{a}{n^k}\right)^{bn^k} \rightarrow e^{ab}$ as $\color{red} n \rightarrow \infty$

$2^n/n^2$

Use sandwich theorem ..

$sin n / \sqrt{n}$

Use sandwich theorem ..

$\sqrt {n^2+n} - n$

can anyone tell me the general methods for simplfing these sequence so it looks more obvious?

..

**running-gag** · March 21st 2010, 12:24 PM

Originally Posted by General

Use sandwich theorem ..

In French we say "policemen theorem"

Thread: determine if they are converge

LinkBack

Thread Tools

Display

determine if they are converge

Similar Math Help Forum Discussions

determine whether the following series converge or diverge

If independent Xn converge in probability they almost surely converge to a constant

Determine whether a sequence converge

Determine whether the series converge.

determine if it's converge

Search Tags