CPM Homework Help : PCT Problem 2-42

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2-42.

Expand each of the following sums and find them.

$\displaystyle \sum _ { n = 1 } ^ { 4 } n ^ { 2 }$
Step (a):
$1^2+2^2+3^2+4^2$

$\displaystyle \sum _ { j = 2 } ^ { 6 } 6 j - j ^ { 2 }$
Step (b):
$(6(2)-2^2)+(6(3)−3^2)+$
$(6(4)-4^2)+(6(5)−5^2)+$
$(6(6)-6^2)$

$\displaystyle \sum _ { i = 3 } ^ { 6 } 3 ^ { i }$
Hint (c):
Follow the same process as shown in parts (a) and (b).
Be sure to note the starting and ending indices!

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