Question

Use sigma notation to represent the following series for the first 10 terms. 3 + (-6) + 12 + (-24) + ⋯

Answer 1

`\sum_(n=0)^(9)(-1)^n\,3\,(2^n)`

Explanation:

Given:
`3+(-6)+12+(-24)+...`

To find: sigma notation to represent the given series for the first 10 terms

Solution:

Sigma notation is a form used to give a general expression for a sum of the values of variables. ∑ is used to denote sum

`x_1+x_2+x_3+...+x_n` can be written as
`x_1+x_2+x_3+...+x_n=\sum_(i=1)^(n)x^i`

`3+(-6)+12+(-24)+...`

Here,

`3=(-1)^03(2^0)\\-6=(-1)^13(2^1)\\12=(-1)^23(2^2)\\-24=(-1)^33(2^3)`

So, sigma notation for the given series for the first 10 terms is
`\sum_(n=0)^(9)(-1)^n\,3\,(2^n)`