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If (1+x)^(n)=sum(r=0)^(n)*C(r )x^(r ) an...

If `(1+x)^(n)=sum_(r=0)^(n)*C_(r )x^(r )` and `sum_(r=0)^(n) (-1)^(r ) (C_(r ))/((r+1)^(2)=k sum_(r=0)^(n)(1)/(r+1)`, then k is equal to :

A

`(1)/(n) `

B

`(1)/(n+1)`

C

`(n)/(n+1)`

D

none

Text Solution

Verified by Experts

The correct Answer is:
b
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ML KHANNA-BINOMIAL THEOREM AND MATHEMATICAL INDUCTION -Problem Set (4) (MULTIPLE CHOICE QUESTIONS)
  1. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+…+C(n)x^(n), then C(0)+5C(1)+9C(2)+...

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  2. If (1+x)^(n)= sum(r=0)^(n)C(r )x^(r ) and sum(r =0)^(n) (C(r ))/(r+1)=...

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  3. If (1+x)^(n)=sum(r=0)^(n)*C(r )x^(r ) and sum(r=0)^(n) (-1)^(r ) (C(r ...

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  4. The sum of the series .^(20)C(0)-.^(20)C(1)+ .^(20)C(2)-.^(20)C(3)+...

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  5. The sum to (n+1) terms of the series (C(0))/(2)-(C(1))/(3)+(C(2))/(...

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  6. If C(r ) stands for ""^(n)C(r ), then the sum of first (n+1) terms of...

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  7. The value of the sum of the series 3.""^(n)C(0)-8" "^(n)C(1)+13" "^(n...

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  8. If (1+x)^(n) = C(0)+C(1)x + C(2) x^(2) +...+C(n)x^(n) then C(0)""^...

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  9. If n is a positive integer and C(k)=""^(n)C(k), then the value of sum(...

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  10. The vaule of sum(r=0)^(n-1) (""^(C(r))/(""^(n)C(r) + ""^(n)C(r +1)) ...

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  11. sum(r=0)^(n) (-1)^(r )" "^(n)C(r ) (1+r x)/(1+n x) equals

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  12. If n gt 3, then abC(0)-(a-1) (b-1) C(1) + (a-2)(b-2) C(2)-(a-3) (b-3) ...

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  13. If C(r) be the coefficients of x^(r) in (1 + x)^(n) , then the value ...

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  14. If n is an odd natural number, then sum(r=0)^(n) ((-1)^(r ))/(""^(n)C(...

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  15. If a(n) = sum(r=0)^(n) (1)/(""^(n)C(r)) , find the value of sum(...

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  16. With usual notations C(0)C(1)+C(1)C(2)+…+C(n-1)C(n)=

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  17. With usual notations C(0)C(2)+C(1)C(3)+C(2)C(4)+…+C(n-2)C(n)=

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  18. With usual notations, C(0)C(r )+C(1)C(r+1) +C(2)C(r+2) +…+C(n-r)C(n)...

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  19. The coefficient of x^(n) y^(n) in the expansion of [(1 + x)(1+y) (x...

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  20. The coefficient of x^r[0lt=rlt=(n-1)] in lthe expansion of (x+3)^(n-1)...

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