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Re: infinite series question
Posted:
Nov 24, 2002 2:39 AM


> 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(n1) + 1/2^(n1) = 2^n1/2^(n1)
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*(1/1r), 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



