Question

What is the sum of the infinite geometric series?

Answer 1

Answer:

The sum of the  infinite geometric series is:

                                 -288

Step-by-step explanation:

We know that the sum of the infinite geometric series:

$\sum_{n=1}^{\infty} ar^{n-1}$

is given by the formula:

$Sum=\dfrac{a}{1-r}$

The series is given by:

     $\sum_{n=1}^{\infty} (-144)\cdot (\dfrac{1}{2})^{n-1}$

By looking at the series we observe that the first term of the series is:

            $a=-144$

and the common ratio of the series is:

$r=\dfrac{1}{2}$

Hence, the sum of the series is:

$Sum=\dfrac{-144}{1-\dfrac{1}{2}}\\\\Sum=\dfrac{-144}{\dfrac{1}{2}}\\\\Sum=-144\times 2\\\\Sum=-288$

Answer 2

Answer:

-288

Step-by-step explanation:

n=1/2 divided by -144. You then just plug that number which is .00347 into n in the equation and use a scientific calculator to find the answer.