Answer to Question #199728 in Calculus for Moe

Question

which of the expressions below are equal to

$4•1 + 7•4 + 10•9 +13•16...$

when summed to the $k$ terms?

1)

$k$

$Σ$ $(a^3 + 3a^2)$

$a = 1$

2)

$k$

$Σ$ $(3a-1)(a^2)$

$a = 1$

3)

$k$

$Σ$ $(3a^3 + a^2)$

$a = 1$

4)

$k(k+1)(9k^2 + 13k +2)$

_________________________

$12$

5)

$k(k+1)(9k^2+2k+13)$

___________________________

4

Answer 1

3)

$\displaystyle\sum_{a=1}^{k}(3a^3+a^2)=\displaystyle\sum_{a=1}^{k}((3a+1)a^2)$

$=4\cdot1+7\cdot4+10\cdot9+13\cdot16+...(3k+1)k^2$