# calculus

sum of the geometric series (2 - 3^n) / 5^n

whats a and r?

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asked by tom
1. its an infinite series by the way

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posted by tom
2. The series is not geometric, as there is no common ratio.
However, it is the difference of two geometric series
(2-3^n)/5^n = 2/5^n - 3^n/5^n = 2(1/5)^n - (3/5)^n
The first series has a = 2/5 and r=1/5
The second series has a = 3/5 and r = 3/5
Now just find the sum of each as usual, and subtract.

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posted by oobleck
3. so s=0?

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posted by tom
4. no. what is your work?
Just plug in S∞ = a/(1-r)

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posted by oobleck
5. i did (2/5)^n and i got 5/2. I did (3/5)^n and i got 5/2. 5/2 - 5/2 = 0

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posted by tom
6. (2/5) / (1 - 1/5) = (2/5) / (4/5) = 1/2
(3/5) / (1 - 3/5) = (3/5) / (2/5) = 3/2
1/2 - 3/2 = -1

You showed some work, but you didn't use the values for a and r that I showed you!

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posted by oobleck
7. how did you get your a and r?

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posted by tom
8. geez - write down the first few terms of each of the geometric sequences.

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posted by oobleck

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