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The sequence {x(k)} is defined by x(k+1)...

The sequence `{x_(k)}` is defined by `x_(k+1)=x_(k)^(2)+x_(k)` and `x_(1)=(1)/(2)`. Then `[(1)/(x_(1)+1)+(1)/(x_(2)+1)+...+(1)/(x_(100)+1)]` (where `[.]` denotes the greatest integer function) is equal to

A

0

B

2

C

4

D

1

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The correct Answer is:
D
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DISHA PUBLICATION-SEQUENCES AND SERIES -Exercise -2 : Concept Applicator
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  2. If a,b,c are in H.P.then which one of the following is true

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  3. If a,b,c and the d are in H.P then find the vlaue of (a^(-2)-d^(-2))/(...

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  4. The odd value of n for which 704 + 1/2 (704) + 1/4 (704) + ... upto n ...

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  5. If (1-p)(1+3x+9x^2+27 x^3+81 x^4+243 x^5)=1-p^6p!=1 , then the value o...

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  6. The harmonic mean of (a)/(1 - ab) and (a)/(1 + ab) is :

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  7. The sum of the infinite series(2^(2))/(2!) + (2^(4))/(4!) + (2^(6))/(6...

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  8. If a,b,c re in H.Pthen which one of the following is true

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  9. ABC is a right angled triangle in which /B=90^(@) and BC=a. If n point...

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  10. If S(1), S(2), S(3),...,S(n) are the sums of infinite geometric series...

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  11. If a is the A.M. of ba n dc and the two geometric mean are G1a n dG2, ...

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  12. If a ,ba n dc are in A.P., and pa n dp ' are respectively, A.M. and G....

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  13. The AM, HM and GM between two numbers are (144)/(15), 15 and 12, but n...

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  14. If the arithmetic geometric and harmonic menas between two positive re...

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  15. If exp (sin^2x+sin^4x +sin^6 x........upto oo)loge 2 satisfies the equ...

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  16. If L(1) = (2.02 +- 0.01)m and L(2) = (1.02 +- 0.01)m then L(1) + 2L(2)...

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  17. sum(k =1)^(n) k(1 + 1/n)^(k -1) =

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  18. The sequence {x(k)} is defined by x(k+1)=x(k)^(2)+x(k) and x(1)=(1)/(2...

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  19. If |x| lt 1,then the sum of the series 1 + 2x + 3x^(2) + 4x^(2) + .......

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  20. The sum of n terms of the series 1^2+2.2^2+3^2+2.4^2+5^2+2.6^2+.... is...

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