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December 15th, 2006, 01:34 PM  #1 
Newbie Joined: Dec 2006 Posts: 28 Thanks: 0  Term of the geometric
Find the sum of the first 10 terms of the geometric series whose first term is 6 and whose common ratio is 2

December 15th, 2006, 04:57 PM  #2 
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Why can't you just use the formula for a geometric series?: a/(1r) (6)/(1(2))=2 
December 16th, 2006, 03:27 AM  #3  
Senior Member Joined: Dec 2006 Posts: 1,111 Thanks: 0  Quote:
2 if r=2, because if r>=1, a geometric series diverges to infinity, and the a/(1r) formula doesn't work. You have to prove that the series converges first before you can find out what it converges to. In this case, the series would diverge by the nth term divergence test, since the lim n>00 of (6)(2)^n =00 .  
December 16th, 2006, 07:44 AM  #4 
Newbie Joined: Dec 2006 Posts: 28 Thanks: 0 
Thank guys very much.. just asking from with lesson is that. i mean what kind of problem is this

January 29th, 2007, 02:13 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,934 Thanks: 2208 
(6 + 12) + (24 + 48) + (96 + 192) + (384 + 768) + (1536 + 3072) = 6 + 24 + 96 + 384 + 1536 = 2046 Sum of n terms = a(1  r^n)/(1r) = 6(1  (2)^n)/(1  (2)) (for the series in the above problem) = 2(1  (2)^n) = (2)^(n+1)  2 = 2^(n+1)  2 if n is even;  2^(n+1)  2 if n is odd. 

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