Originally Posted by

**HyunGyum** The question I have is....

Using induction, verify the inequality

$\displaystyle (1+x)^n$ is greater than or equal to (1+nx)

for x is greater than or equal to -1 and n is greater than or equal to 1

The basis step was easy enough (as always)

However, I became stuck at the induction part...

Since the condition given is for BOTH x AND n, I tried doing induction for

x+1 and n+1

So I had the following...

Assuming the above statement to be true, prove

(2+x)^(n+1) is greater than or equal to 1+(n+1)(x+1)

I tried a lot of different ways, but couldn't solve it...

Any hints/tips on how to solve an induction problem with two changing variables?