Question

Find the sum of the following infinite geometric series.

Answer 1

Answer:

Final answer is $\frac{80}{3}$.

Step-by-step explanation:

We have been given an infinite geometric series.

Now we need to find it's sum.

common ratio $r=-\frac{1}{5}$.

plug n=1 to get the first term

$a_n=32\left(-\frac{1}{5}\right)^{\left(n-1\right)}$

$a_1=32\left(-\frac{1}{5}\right)^{\left(1-1\right)}$

$a_1=32\left(-\frac{1}{5}\right)^{\left(0\right)}$

$a_1=32\left(1\right)$

$a_1=32$

Now plug these values into infinite sum formula

$S_{\infty}=\frac{a_1}{1-r}=\frac{32}{1-\left(-\frac{1}{5}\right)}=\frac{32}{1.2}=\frac{320}{12}=\frac{80}{3}$

Hence final answer is $\frac{80}{3}$.