discrete mathematics - Proving an inequality by mathematical induction

I'm trying to solve a problem with inequalities using mathematical induction but I am stuck halfway through the process.

The problem: Use mathematical induction to establish the inequality -
$(1 + \frac{1}{2})^n \ge 1 + \frac{n}{2}$ for n $\in \mathbb{N}$

Steps

1) $n = 1$, $(1 + \frac{1}{2})^1 \ge 1 + \frac{1}{2}$ is TRUE

2) $n = k$, assume that $(1 + \frac{1}{2})^k \ge 1 + \frac{k}{2}$ for n $\in \mathbb{N}$

3) Show the statement is true for $k + 1$

$(1 + \frac{1}{2})^{k+1}$ = $(1 + \frac{1}{2})^k * (1 + \frac{1}{2})$

$\ge$ $(1 + \frac{k}{2}) * (1 + \frac{1}{2})$ - using the assumption in step $2$

My question is, how do I continue this problem? Or did I go wrong somewhere? I just can't figure out what the next step is.

Answer

Continue with:

$(1 + \frac{k}{2}) * (1 + \frac{1}{2}) =$

$1 + \frac{k}{2} + \frac{1}{2} + \frac{k}{4} >$

$1 + \frac{k}{2} + \frac{1}{2}=$

$1 + \frac{k+1}{2}$