prove monotonicity of a sequence

**hedi** · December 5th 2012, 08:59 AM

Prove that the sequence (1+1/n)^(n+1) is monotonically decreasing,without using functions and derivatives.

**emakarov** · December 5th 2012, 09:34 AM

See here.

**Plato** · December 5th 2012, 11:18 AM

Originally Posted by hedi

Prove that the sequence (1+1/n)^(n+1) is monotonically decreasing,without using functions and derivatives.

$\begin{align*}\left( {1 - \frac{1}{n}} \right)^n\left( {1 + \frac{1}{n}} \right)^n&= \left( {1 - \frac{1}{n^2}} \right)^n \ge\left( {1 - \frac{1}{n}} \right)\\ \left( {1 + \frac{1}{n}} \right)^n &\ge \left( {1 - \frac{1}{n}} \right)^{1-n}\\\left( {1 + \frac{1}{n}} \right)^n &\ge\left( {1 + \frac{1}{n-1}} \right)^{n-1} \end{align*}$ .

**hedi** · December 5th 2012, 11:57 AM

Thank's but this is not the right sequence.The given sequence is monotonically decreasing

Thread: prove monotonicity of a sequence

LinkBack

Thread Tools

Display

prove monotonicity of a sequence

Re: prove monotonicity of a sequence

Re: prove monotonicity of a sequence

Re: prove monotonicity of a sequence

Similar Math Help Forum Discussions

Monotonicity

monotonicity

Monotonicity

prove that if sequence (an) converges, use def of limit of sequence to prove...

Monotonicity of a sequence

Search Tags