# Math Help - Induction help

1. ## Induction help

I am stuck on this proof, but this is what i have done so far.

When n=1 it is ture as (1+a)^1>= 1+a

we can know assume P(k) is true:

(1+a)^k>= 1+Ka

so for P(K+1)= (1+a)^k+1>= (1+Ka)(1+K)
>= (1+k+ka+k^2a)

this looks wrong to me and i cannot figure it out on how to finish this proof can so one please help me.

Thanks

2. Start with $\left( {1 + a} \right)^K \geqslant 1 + Ka$ being true.
Then go to the next step:
$\begin{array}{rcl}
{\left( {1 + a} \right)^{K + 1} } & = & {\left( {1 + a} \right)^K \left( {1 + a} \right)} \\
{} & \geqslant & {\left( {1 + Ka} \right)\left( {1 + a} \right)} \\
{} & = & {1 + a + Ka + Ka^2 } \\
{} & > & {1 + a + Ka,\,\,({\color{blue}Ka^2 > 0)}} \\
{} & = & {1 + \left( {K + 1} \right)a} \\ \end{array}$