Originally Posted by

**Volga** I have come across this 'simple' question in more than one book on proofs, yet I am not able to find a solution:

Prove, for all $\displaystyle n\geq0$, that $\displaystyle (1+x)^n\geq1+nx$ if $\displaystyle 1+x>0$.

I can see how this fact can be demonstrated via binomial theorem

$\displaystyle (1+x)^n=1+nx+\frac{n(n-1)}{2}x^2+...$

(since the first third component of the expansion is always non-negative)

but could you give me a hint how to go about proving it using proof by induction?

thanks