I am still having trouble following the simplification of equations in the Induction examples i am studying.

The notes I have use this:

$\displaystyle

[\frac{1}{2}k(k+1)] + (k+1)

$

which is simplified to

$\displaystyle

\frac{1}{2}(k+1)[(k+1)+1]

$

but when I do the math I get

$\displaystyle

[\frac{1}{2}k(k+1)] + (k+1) = [\frac{1}{2}k^2 + k] + (k+1) = [\frac{1}{2}k^2 + k] + (k+1)

$

so if anyone could explain the steps used in the former expression I would me much appreciative