Posted by Mercy on Wednesday, May 30, 2007 at 4:42pm.
Can someone please help me with this problem? Thanks!
Evaluate the infinite geometric series:
8+4+2+1+...
I thought you needed to know the number of terms to evaluate, but how do you know them if it is infinite?
The limit of Sn = 1 + r + r^2 + r^3 + r^4 + = 1/(1 - r) -1 < r < 1
Therefore, the sum of the series 8, 4, 2, 1, 1/2, 1/4, 1/8, ....becomes 8 + 4 + 2 + 1/(1 - 1/2) = 16
I'm not quite sure I understand your formula. The formula I received for geometric series is Sn=a1 (1-r^n)/(1-r) where a1 is the first term and r is what you multiply by and n is given or is the number of terms.
Is the -1 < r < 1 the same as what we got: |r| < 1, which means it is convergent and |r| > or = 1 so it is divergent?
While it is a geometric series, it is a converging series with an infinite number of terms.
The limit, or number that the series converger on is 1/( - r) where -1<r<+1.
Applying Sg = a(r^n - 1)/(r - 1) yields
Sg = 8[(1/2)^inf. - 1]/(1/2 - 1) =
8[0 - 1]/(-1/2) = (-8)/(-1/2) = 16.
I am really confused.
This formula you gave: a(r^n - 1)/(r - 1) is very similar to mine: a1 (1-r^n)/(1-r).
Is your way the only way to do it? Do you know how to do it the way my teacher taught?
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