Question

I'm not sure how to write this out, Please help me and explain this.Thanks

Answer 1

Let's find the sum of the series:

`\sum ^(11)_(n\mathop=1)(3+2n)`

We'll use these formulas

`\begin{gathered} \sum ^n_1K=K\cdot n \\ \sum ^(i=n)_(i=1)i=(n(n+1))/(2) \end{gathered}`

We separate the series in two:

`S_1=\sum ^(11)_(n\mathop=1)3=3\cdot11=33`
`S_2=\sum ^(i=11)_(i\mathop=1)2\cdot i=2\sum ^(i=11)_{i\mathop{=}1}i=2\cdot(11\cdot(11+1))/(2)=11\cdot12=132`

Thus, our sum is

S = 33 + 132 = 165