Evaluate $\sum _ { k = 1 } ^ { 20 } \left( k ^ { 3 } + 6 \right)$ using the summation formulas and properties.
A) $44,100$
B) $8,006$
C) $176,520$
D) $44,220$
E) $176,400$

Question

Quizplus · Accepted Answer

The sum can be split as $\sum_{k=1}^{20} k^3 + \sum_{k=1}^{20} 6$. The first part is $(\sum_{k=1}^{20} k)^2 = (210)^2 = 44,100$. The second part is $6 \times 20 = 120$. Adding them gives $44,220$.

Evaluate ∑k=120(k3+6)\sum _ { k = 1 } ^ { 20 } \left( k ^ { 3 } + 6 \right)∑k=120​(k3+6)

Evaluate $\sum _ { k = 1 } ^ { 20 } \left( k ^ { 3 } + 6 \right)$