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clavezza
New Member

USA
2 Posts

Posted - 08/31/2007 : 23:17:01

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

Ultraglide
Advanced Member

Canada
278 Posts

Posted - 09/01/2007 : 00:42:41

I'm not sure what your problem is, could you clarify it?

Ultraglide
Advanced Member

Canada
278 Posts

Posted - 09/01/2007 : 00:43:54

Is it a summation? Are you proving by induction?

Subhotosh Khan
Advanced Member

USA
9114 Posts

Posted - 09/01/2007 : 12:23:35

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.

clavezza
New Member

USA
2 Posts

Posted - 09/01/2007 : 12:35:00

SOrry,

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

chris

sahsjing
Advanced Member

USA
2399 Posts

Posted - 09/01/2007 : 19:51:07

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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