Question

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

25 + 5 + 1 + . . .

Answer 1

Answer:

  31.25

Step-by-step 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

Answer 2

If we factor 25 from the sum, we have

$\displaystyle 25\left(1+\dfrac{1}{5}+\dfrac{1}{25}+\ldots\right)=25\sum_{i=0}^\infty \left(\dfrac{1}{5}\right)^i = 25 \dfrac{1}{1-\frac{1}{5}} = 25\dfrac{1}{\frac{4}{5}}=25\cdot \dfrac{5}{4} = \dfrac{125}{4}$