anonymous one year ago Evaluate the series 50 + 10 + 2 + . . .

1. anonymous

I'm confused as to what "Evaluate" actually means. Answer choices: A) 62 B) 1/5 C) The series diverges; it does not have a sum D) 62.5

2. SolomonZelman

you divide by 5 every time. you start from 50 so you can write it as $$\large\color{black}{ \displaystyle \sum_{ n=0 }^{ \infty } ~ \dfrac{50}{5^n}}$$

3. SolomonZelman

this series definitely converges, will you give me that?

4. anonymous

Yeah

5. SolomonZelman

you can find the exact sum because it is geometric...

6. SolomonZelman

$$\Large\displaystyle\sum_{ n=0 }^{ \infty } ~ 50(1/5)^n=\frac{50}{1-\frac{1}{5}}=?$$

7. anonymous

we would get 125/2 or 62.5. Thanks. Is there any place where i could get a quick refresher on Geometric and arithmetic series?

8. anonymous

That is correct