Asked by tom
sum of the geometric series (2 - 3^n) / 5^n
whats a and r?
whats a and r?
Answers
Answered by
tom
its an infinite series by the way
Answered by
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.
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.
Answered by
tom
so s=0?
Answered by
oobleck
no. what is your work?
Just plug in S∞ = a/(1-r)
Just plug in S∞ = a/(1-r)
Answered by
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
Answered by
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!
(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!
Answered by
tom
how did you get your a and r?
Answered by
oobleck
geez - write down the first few terms of each of the geometric sequences.
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