Question

Use the properties of sigma notation and the summation formulas to evaluate

Answer 1

Since the given question is

$\sum_{i\mathop{=}1}^{10}(i^2+3i-2)$

We will substitute i by 1 to 10, then add all the answers

$\begin{gathered} 1^2+3(1)-2=2 \\ 2^2+3(2)-2=8 \\ 3^2+3(3)-2=16 \\ 4^2+3(4)-2=26 \\ 5^2+3(5)-2=38 \end{gathered}$$\begin{gathered} 6^2+3(6)-2=52 \\ 7^2+3(7)-2=68 \\ 8^2+3(8)-2=86 \\ 9^2+3(9)-2=106 \\ 10^2+3(10)-2=128 \end{gathered}$

Now, we will add the answers

$\sum_{i\mathop{=}1}^{10}(2+8+16+26+38+52+68+86+106+128)=530$

The answer is the 1st choice