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Sequence question

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Sequence question

by gmataug08 » Wed Nov 26, 2008 6:45 pm
In the infinite sequence A, An= X^(n-1) + X^(n) + X^(n+1) + X^(n+2) + X^(n+3)
where x is a positive integer constant. For what value of n is the ratio
of An to X(1+X(1+X(1+X(1+X)))) equal to X^5 ?

(A) 8
(B) 7
(C) 6
(D) 5
(E) 4
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by cramya » Wed Nov 26, 2008 8:27 pm
I simplified X(1+X(1+X(1+X(1+X)))) to

x+x^2+x^3+x^4+x^5

Then multiplied this by x^5 to get
x^6+x^7+x^8+x^9+x^10 and the only value to get this is n=7

x5(x+x^2+x^3+x^4+x^5) / x+x^2+x^3+x^4+x^5

= x^5

B)
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by gmataug08 » Wed Nov 26, 2008 9:44 pm
OA is B
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