Question

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

whats a and r?

Answers

tom
its an infinite series by the way
oobleck
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.
tom
so s=0?
oobleck
no. what is your work?
Just plug in S∞ = a/(1-r)
tom
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
oobleck
(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!
tom
how did you get your a and r?
oobleck
geez - write down the first few terms of each of the geometric sequences.

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