Question

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

Answer 1

Answer:

$\sum_{n=0}^{9}(-1)^n\,3\,(2^n)$

Step-by-step 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 $\sum_{n=0}^{9}(-1)^n\,3\,(2^n)$