Question

I need help with sigma notation :/

Answer 1

\[\sum_{n=1}^{7}2(-2)^{n-1}\]

Answer 2

would you like to expand that?

Answer 3

I'm not sure how to solve it or anything. My lesson didn't explain what to do very well :/ So I'm completely lost

Answer 4

$$\Large{ \sum_{n=1}^{7}2(-2)^{n-1}
\\~\\ = 2(-2)^{\color{red}1-1} +2(-2)^{\color{red}2-1} +2(-2)^{\color{red}3-1}
\\ + 2(-2)^{\color{red}4-1} + 2(-2)^{\color{red}5-1} + 2(-2)^{\color{red}6-1}
\\ + 2(-2)^{\color{red}7-1}



}
$$

Answer 5

So the answer would be 86?

Answer 6

so the sigma is shorthand for all that.
but there is a closed formula so you dont have to add these up all manually

Answer 7

yes thats correct

Answer 8

Thank you so much :)