Question

How do you find the sum of the convergent series 10-5/2+5/8-...? If the convergent series is not convergent, how do you know?

Answer 1

Yes, it is convergent because `abs(r)<1`

Explanation:

`r=(-5/2)/10=-1/4`

`abs(-1/4)<1`, so it is convergent

`"infinite geometric sum" = a_1/(1-r)=10/(1-(-1/4))=8`

hope that helped