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Expert: - 1/20/2009


Question
Dear Sir/Sirs
I want a the solution for the following serious :
N : non zero even positive integer
Vo is the intial value of a certain product for example
what is VN if the following occurs :
when N=2
V2=0.172 * Vo * 1.1^0
V4=0.172 * Vo * (1.1^0 + 1.1^2)
V6=0.172 * Vo * (1.1^0 + 1.1^2 + 1.1^4)
V8=0.172 * Vo * (1.1^0 + 1.1^2 + 1.1^4 + 1.1^6)

thanks in advance

Answer
I will assume that N is always positive and even,
since that is what I have been given.  It can be seen that
VN = 0.172*V0*Σ1.1^(2(n-1)) where the Σ goes from n=1 to N/2.

The summation is (1.1^0 + 1.1^2 + 1.1^4 +  ... + 1.1^N), which can
be rewritten  as [1.21^0 + 1.21^1 + 1.21^2 + ... + 1.21^(N/2)].

If we multiply by (1 - 1.21), all of the middle terms cancel and
we get 1.21^0 - 1.21^(1 + N/2), which is 1 - 1.21^(1 + N/2).

This means the final equation to use is
VN = 0.172 * V0 * [1 - 1.1^(1 + N/2)]/(1 - 1.21).

Your welcome.  It was fun.

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