1. Jan 27, 2008

wowolala

the quesion is below, show that
show that ( 1+ $$\frac{x}{n}$$ ) ^n < e^x

at the first, i take log on both sides,.. but i couldn't go further.

can someboday help me?

thx

2. Jan 27, 2008

EnumaElish

What do you get when you apply log to both sides?

3. Jan 27, 2008

mathman

Expand the lhs by the binomial theorem and take the power series for e^x. The solution becomes obvious for x>0. For x<0, it is a little trickier - work with terms 2 at a time.

Last edited: Jan 27, 2008
4. Jan 27, 2008

thx so much