Question

6. Use the formula to evaluate the infinite series. Round to the nearest hundredth if necessary.9 + 3+1+...a1S =1-5Formula for a converging infinite series. a, is the first term and r is the common ratio.13.5R3274.5

Answer 1

The formula given

`\begin{gathered} s=(a_1)/(1-r) \\ \text{where a}_1=\text{ first term and r= common ratio} \end{gathered}`

Can be used to find the sum to infinity of a series as shown below

Step 1: Write out the sequence

9 + 3 + 1 ...

Step 2: Obtain the first term and common ratio

`\begin{gathered} a_(1=)\text{first term=9} \\ \text{common ratio=r=}\frac{\sec ond\text{ term}}{first\text{ term}}=(3)/(9)=(1)/(3) \end{gathered}`

Step 3: Substitute the value of the first term and common ratio into the equation

`s=(9)/(1-(1)/(3))`

`s=(9)/((2)/(3))`

`s=9\text{ x }(3)/(2)`
`s=(27)/(2)`
`s=13.5`

Answer = 13.5