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Topic: infinite series question
Replies: 3   Last Post: Nov 24, 2002 12:18 PM

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Randall L. Rathbun

Posts: 62
Registered: 12/6/04
Re: infinite series question
Posted: Nov 24, 2002 2:39 AM
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> S1 = 1 = 1/1
> S2 = 1 + 1/2 = 3/2
> S3 = 1 + 1/2 + 1/4 = 7/4
> S4 = 1 + 1/2 + 1/4 + 1/8 = 15/8 (not 9/8)

S5 = S4 + 1/16 = 31/16
S6 = S5 + 1/32 = 63/32
...
Sn = S(n-1) + 1/2^(n-1) = 2^n-1/2^(n-1)

I think you can see what is going on here.

The sum is getting closer and closer to 2.
The infinite sum is 2.

The sum of a geometric series with the ratio of 1/r between each term is
a*(1/1-r), where a is the first term. In this case, a=1 and r=2 so

Sum = 1*(1/(1/2) = 1*2 = 2

You can also see that if r approaches 1, then the sum climbs towards
infinity.

Randall




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