#### Answer

$a. 1^{2} $
$b. k^{2}$
$c. 1 + 3 +5 + ... + [2(k+1)-1]$
$d. (k+1)^{2}$
$e.$ the odd integer just before $2k+1$ is $2k-1$
$f.$ inductive hypothesis

#### Work Step by Step

Fill the answers with inductive step by using proof by mathematical induction.