Originally Posted by

**surjective** Hello again,

Sorry for the inconvenience. The thing is that what you mentioned before is exactly what I have already done . . . and then I get stuck. I can't seem to get the "great idea" (maybe because I havn't slept all night).

What I'm trying to do is to reach the conslusion (instead of showing the truthfulness of an inequality):

$\displaystyle (1+x)^{n+1} \geq 1+(n+1)x $

Now from calculus I know that:

$\displaystyle (1+x)^{n+1}= (1+x)^{n}(1+x) $

Using the inductive step we may write:

$\displaystyle (1+x)^{n}(1+x) \geq (1+nx)(1+x) $

This is where I get stuck.

Your help is greatly appreciated.

Thanks.