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Number Systems -Sequence and Series

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Number Systems -Sequence and Series

by sukhman » Thu Oct 17, 2013 10:24 am
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 ganeshrkamath » Thu Oct 17, 2013 7:53 pm
sukhman wrote: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
The highest power of x in x(1 + x(1 + x(1 + x(1 + x)))) is 5.
The highest power of x in A(n) is (n+3)
When A(n) is divided by the given term, we get x^5.

(n+3) = 5 + 5
n = 7

Choose B

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by sukhman » Thu Oct 17, 2013 9:26 pm
Sorry put the wrong statement in wrong post!!
Last edited by sukhman on Fri Oct 18, 2013 12:55 am, edited 1 time in total.
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by ganeshrkamath » Thu Oct 17, 2013 11:18 pm
sukhman wrote:I did not understand what I got was 3^11.5^11=5*x^11 is this equation right ?
Can you elaborate your method?

Alternate approach:
An = (x(1 + x(1 + x(1 + x(1 + x))))) * x^5
= (x(1 + x(1 + x(1 + x + x^2)))) * x^5
= (x(1 + x(1 + x + x^2 + x^3))) * x^5
= (x(1 + x + x^2 + x^3 + x^4)) * x^5
= (x + x^2 + x^3 + x^4 + x^5)) * x^5
= x^6 + x^7 + x^8 + x^9 + x^10

Also,
An = x ^(n - 1) + x^n + x^ (n + 1 ) + x ^ (n + 2)+ x^ (n + 3)

So (n+3) = 10
n = 7

Hope this helps.

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