Question

What is the value of the summation ∑i=14(2i+6i2)?

180

200

220

240

I think it's C

Answer 1

uh

Answer 2

@micahm: Your expression ∑i=14(2i+6i2) does not appear to be properly formed. Please double check to ensure that you are copying the original problem correctly. Consider presenting the problem as a drawing (using the Draw utility, below).

Answer 3

Here are some useful formulas:
\[\sum_{i=1}^ni=\frac{n(n+1)}{2}\\
\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}{6}\]
Also, use the fact that summations are linear operators:
\[\sum_{i=1}^n(ai+bi^2)=a\sum_{i=1}^ni+b\sum_{i=1}^ni^2\]
\[\begin{align*}\sum_{i=1}^{14}(2i+6i^2)&=2\sum_{i=1}^{14}i+6\sum_{i=1}^{14}i^2\\
&=2\times\frac{14\times15}{2}+6\times\frac{14\times15\times29}{6}
\end{align*}\]