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clavezza
New Member

USA
2 Posts

Posted - 08/31/2007 :  23:17:01  Show Profile
I am not sure how to solve this particular problem:

2 + 6 + 18 + ... + 2 * 3 to the n-1 power = 3n - 1



Thanks for the help

Chris
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Ultraglide
Advanced Member

Canada
299 Posts

Posted - 09/01/2007 :  00:42:41  Show Profile
I'm not sure what your problem is, could you clarify it?
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Ultraglide
Advanced Member

Canada
299 Posts

Posted - 09/01/2007 :  00:43:54  Show Profile
Is it a summation? Are you proving by induction?
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Subhotosh Khan
Advanced Member

USA
9117 Posts

Posted - 09/01/2007 :  12:23:35  Show Profile
quote:
Originally posted by clavezza

I am not sure how to solve this particular problem:

2 + 6 + 18 + ... + 2 * 3 to the n-1 power = 3n - 1



Thanks for the help

Chris



Factor out 2 - then you have a GP series.
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clavezza
New Member

USA
2 Posts

Posted - 09/01/2007 :  12:35:00  Show Profile
SOrry,

Suppose to use mathematical induction to prove that the statements are true for every positive integer n.

chris
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sahsjing
Advanced Member

USA
2399 Posts

Posted - 09/01/2007 :  19:51:07  Show Profile
n = 1
2 = 3^(1)-1 It works.
Assume at n = k, 2 + 6 + 18 + ... + 2 * 3 ^(k-1) = 3^(k) - 1
At n = k+1,
2 + 6 + 18 + ... + 2 * 3 ^k
= 2 + 6 + 18 + ... + 2 * 3 ^(k-1) + 2*3^k
= 3^(k) - 1 + 2*3^k
= 3^k(1+2)-1
= 3^(k+1) - 1

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