This is from [this website](http://www.analyzemath.com/math_induction/mathematical_induction.html):

> 
> Use mathematical induction to prove that 
>  $$1 + 2 + 3 +\cdots+ n = \frac{n (n + 1)}{2}$$
>  for all positive integers $n$.
> 
> 
> Solution to Problem 1: Let the statement $P(n)$ be 
>  $$1 + 2 + 3 + \cdots + n = \frac{n (n + 1)}{2}.$$
> 
> 
> STEP 1: We first show that $P(1)$ is true. 
> 
> 
> Left Side $= 1$
> 
> 
> Right Side $= \frac{1 (1 + 1)}{2} = 1$
> 
> 
> Both sides of the statement are equal hence $P(1)$ is true. 
> 
> 
> STEP 2: We now assume that $P(k)$ is true  
> 
>  $$1 + 2 + 3 + \cdots + k = \frac{k (k + 1)}{2}$$
>  and show that $P(k + 1)$ is true by adding $k + 1$ to both sides of the above statement 
>  $$
> \begin{align}
> 1 + 2 + 3 + \cdots + k + (k + 1) &= \frac{k (k + 1)}{2} + (k + 1) \\
> &= (k + 1)\left(\frac{k}{2} + 1\right) \\
> &= \frac{(k + 1)(k + 2)}{2}
> \end{align}
> $$
>  The last statement may be written as 
>  $$1 + 2 + 3 + \cdots + k + (k + 1) = \frac{(k + 1)(k + 2)}{2}$$
>  *Which is the statement $P(k + 1)$.*
> 
> 
> 

My question is how in the very last line is the statement $P(k + 1)$ equal to $\frac{(k + 1)(k + 2)}{2}$. I don't get the last step.