Hi guys

Need help with this proof buy induction.

SOLUTION:

*obviously true*

induction step:

ok here's the problem.

i understand $(1+x)^{n+1}=(1+x)\cdot(1+x)^n$ by law of exponentials

but then this : $\geq (1+x)(1+nx)$ ???? I mean where does this come from: $ (1+x)(1+nx)$

You are assuming that P(n) is true ie so that
obviously in the hypothesis we have $(1+x)^n\geq1+nx$ ... But how to get from $(1+x)^n\geq1+nx$ to $(1+x)^{n+1} \geq (1+x)(1+nx)$ ?? I tried to sub-in $n+1$ and it didnt work..

$(1+(n+1)x) = nx + x + 1 = ????$

How to get from here to $(1+x)(1+nx)$ ????

Obviously im missing something

Thank u guys