Question

Use the formula to evaluate the infinite series. Round to the nearest hundreth if necessary.

25 + 5 + 1 + . . .

Answer 1

If we factor 25 from the sum, we have

`\displaystyle 25\left(1+(1)/(5)+(1)/(25)+\ldots\right)=25\sum_(i=0)^\infty \left((1)/(5)\right)^i = 25 (1)/(1-(1)/(5)) = 25(1)/((4)/(5))=25\cdot (5)/(4) = (125)/(4)`

Answer 2

31.25

Explanation:

The initial term is 25 and the common ratio is 5/25 = 1/5. The formula tells you the sum is ...

25/(1 -1/5) = 25/(4/5) = 31.25