Geometric series sum

[EllieJones]

Hello everyone, I'm trying to do my calculus 2 homework about series, but I got stuck with 2 problems. In the first one down below, I found all the terms however I couldn't find the common ratio therefore I couldn't find the series sum. I already know the series converges, but I couldn't find the sum at all! For the second problem, I literally couldn't understand anything as I remember little from calculus 1 logarithms. I would really appreciate it if you guys helped.

 

[skeeter]

1. two infinite geometric series with [MATH]|r|<1[/MATH]
[MATH]3\sum_{n=0}^\infty \left(\dfrac{1}{2}\right)^n + \sum_{n=0}^\infty \left(-\dfrac{1}{5}\right)^n[/MATH]
2. check the partial sums ... recall [MATH]\ln\left(\dfrac{a}{b}\right) = \ln{a} - \ln{b}[/MATH]

 

[Deleted member 4993]

Hello everyone, I'm trying to do my calculus 2 homework about series, but I got stuck with 2 problems. In the first one down below, I found all the terms however I couldn't find the common ratio therefore I couldn't find the series sum. I already know the series converges, but I couldn't find the sum at all! For the second problem, I literally couldn't understand anything as I remember little from calculus 1 logarithms. I would really appreciate it if you guys helped.
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