Dear All
Can you please let me know how can I calculate the summation of the following series when n approaches infinity?
Sn=1/2 + 1/3 + 2/9 + ... + an
where an = (2^(n2))/(3^(n1))
Thank you
series sum?
Re: series sum?
Starting from the second term, this is a geometric series with ratio = 2/3. Hence the summation equals the first term divided by 1  the ratio.
So 1/3 + 2/9 + ... = (1/3)/(1(2/3)) = 1
The entire series 1/2 + 1/3 + 2/9 + ... = 1/2 + 1 = 3/2
So 1/3 + 2/9 + ... = (1/3)/(1(2/3)) = 1
The entire series 1/2 + 1/3 + 2/9 + ... = 1/2 + 1 = 3/2

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 Joined: Thu Dec 30, 2010 4:36 am
Re: series sum?
Thank you very much for your help. I got the point.
Re: series sum?
You don't really need to treat the first term separately if you don't want to  the whole thing is a geometric series. That is, rather than multiplying 1/3 by 3 and adding 1/2, giving 3/2, you could just multiply the first term, 1/2, by 3, to get 3/2.
Re: series sum?
Yes, you are right, the whole series is geometric. With the first term equal to 1/2, the whole sum is (1/2)/(1/3) = 3/2.