Question

PLEASE HELP ME ASAP

Answer 1

The series is a convergence series and the sum of the series is -8/3

The type of the series

The series is given as:

$\sum\limits^{\infty}_{n = 1} -4(-\frac 12)^{n-1}$

The above series has the following properties:

• First term; a = -4
• Common ratio, r = -1/2

Start by calculating the absolute value of the common ratio

Absolute value = |-1/2|

This gives

Absolute value = 1/2

The above value is less than 1.

It means that the series converges.

The sum of the series

This is calculated using:

$S_{\infty} = \frac{a}{1 -r}$

So, we have:

$S_{\infty} = \frac{-4}{1 + \frac 12}$

Evaluate the sum

$S_{\infty} = \frac{-4}{\frac 32}$

Evaluate the quotient

$S_{\infty} = \frac{-8}{3}$

Hence, the sum of the series is -8/3

Read more about geometric series at:

brainly.com/question/24643676

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