CPM Homework Help : PCT Problem 2-30

Brian has the following sums to find:

$\begin{array}{l} 1 + 3 \\ 1 + 3 + 5 \\ 1 + 3 + 5 + 7 \\ \qquad \quad \; . \\ \qquad \quad \; . \\ \qquad \quad \; . \\ 1 + 3 + 5 + 7 + \dots + 101 \end{array}$

Find a shortcut so that he will not have to add the last sum by hand.

Hint 1:

$1+3=4$ or $2^2$ (How many terms are in the sum?)

Hint 2:

$1+3+5=9$ or $3^2$ (How many terms are in the sum?)

Hint 3:

$1+3+5+7=16$ or $4^2$ (How many terms are in the sum?)

Hint 4:

(How many terms are in the final sum?)