CPM Homework Help : A2C Problem 12-66

Use algebra to demonstrate that each pair of expressions in parts (a) and (b) below are equivalent.

$\frac { k ( k + 1 ) } { 2 } + k + 1$ and $\frac { ( k + 1 ) ( k + 2 ) } { 2 }$
Hint (a):
Simplify and find a common denominator in the first expression:
$\frac{k^2+k+2k+2}{2}$
Now combine like terms and factor.

$\frac { k ( 7 k - 1 ) } { 2 } + 7 ( k + 1 ) - 4$ and $\frac { ( k + 1 ) ( 7 k + 6 ) } { 2 }$
Hint (b):
Use the same method as in part (a).