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The geometric series formula I am using is for an algorithmic analysis problem: $$\frac{a(1-a^n)}{1-a}.$$

If $a = -\frac{5}{6}$, what is the solution in its most simplified form?


My answer is :

   [-5/6.(1 - (-5/6)^n)] / [1 - (-5/6)]
=> [-5/6.(1 + (5/6)^n)] / [1+(5/6)]
=> -5/6.(1+(5/6)^n) * 6/11
=> -5/11.(1+(5/6))^n)

This is what I think the answer is - and I know this isn't difficult - but I haven't done maths in over 10 years and need someone to take me through this example so I can study it and learn from it. Please don't close.

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closed as too localized by Aryabhata, Eric Naslund, t.b., Jonas Meyer, J. M. Apr 17 '11 at 0:43

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This is not particularly difficult. Would you like to show us what you think it might be, and then we can check? –  Henry Apr 12 '11 at 14:50
Plug in, simplify. You can then ask us if that's the right answer; but this is basic arithmetic (not even algebra at this point). –  Arturo Magidin Apr 12 '11 at 14:59
-1: And I have voted to close as too localized. –  Aryabhata Apr 12 '11 at 15:15
Your calculation is OK except for the fact that you can't take the minus sign out of $(-5/6)^n$; this is $(-1)^n(5/6)^n$, which is $-(5/6)^n$ if $n$ is odd, but $+(5/6)^n$ if $n$ is even. –  joriki Apr 12 '11 at 16:21
If it's a calculation you want to verify, just plug it into wolframalpha.com –  Brian Vandenberg Apr 12 '11 at 16:33

1 Answer 1

up vote 0 down vote accepted

As an answer that summarizes the method described in user9492's questions:

The general procedure for your recurrences is given here. This link goes into great depth on the method you're learning about.

Also, the formula above can be found on page 27. This should help make everything more clear.

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