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# Is 1+X+X^2+X^3+X^4+X^5<1/(1-X)? a. X>0 b. X<1 I

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Is 1+X+X^2+X^3+X^4+X^5<1/(1-X)? a. X>0 b. X<1 I [#permalink]  17 Mar 2004, 14:04
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Is 1+X+X^2+X^3+X^4+X^5<1/(1-X)?
a. X>0
b. X<1

I think this problem was discussed on this forum before but I do not remember.
Senior Manager
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[#permalink]  17 Mar 2004, 14:18
(1-x^6)/(1-x) < 1/(1-x)

-x^6/(1-x) < 0
(1-x) >0
x < 1

its B
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[#permalink]  17 Mar 2004, 14:24
Could u please explain how did you get (1-x^6)/(1-x)
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[#permalink]  17 Mar 2004, 14:29
(1-x^n) = (1-x)(1+x+x^2+...+x^(n-1))

Or you can use geometric series formulaes.

S = a + ar+ ar^2+...+ar^(n-1)
rS = ar+ar^2+...+ar^n
S(1-r) = a(1-r^n)

S = a(1-r^n)/(1-r)
[#permalink] 17 Mar 2004, 14:29
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# Is 1+X+X^2+X^3+X^4+X^5<1/(1-X)? a. X>0 b. X<1 I

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