Question

Find the sum of the following infinite geometric series.5+2.5+1.25 +0.625+ ...

Answer 1

10

Step-by-step explanation:

The formula for calculating the sum to infinity of a GP is expressed as;

`S_(\infty)=(a)/(1-r)`

a is the first term

r is the common ratio

From the given sequence;

First-term a = 5

Common ratio r = 2.5/5 = 1.25/5 = 0.5

Substitute the given values into the formula

`\begin{gathered} S_{\infty\text{ }}=\text{ }(5)/(1-0.5) \\ S_(\infty)=(5)/(0.5) \\ S_(\infty)=\text{1}0 \end{gathered}`

Hence the sum to infinity of the series is 10