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

If ` (1 + x)^(n) = sum_(r=0)^(n) C_(r) x^(r),(1 + (C_(1))/(C_(0))) (1 + (C_(2))/(C_(1)))...(1 + (C_(n))/(C_(n-1))) ` is equal to

A

`(n^(n-1))/((n-1)!)`

B

`((n+1)^(n-1))/((n-1)!)`

C

`((n+1)^(n))/(n !)`

D

`((n+1)^(n+1))/(n !)`

Text Solution

Verified by Experts

The correct Answer is:
c
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ML KHANNA-BINOMIAL THEOREM AND MATHEMATICAL INDUCTION -Problem Set (4) (MULTIPLE CHOICE QUESTIONS)
  1. The sum of last ten coefficients in the expansion of (1+x)^(19) when ...

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  2. If S=(1)/(2) ""^(10)C(0) -""^(10)C(1) +2""^(10)C(2)-2^(2)" "^(10)C(3)…...

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  3. If (1 + x)^(n) = sum(r=0)^(n) C(r) x^(r),(1 + (C(1))/(C(0))) (1 + (C(...

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

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  5. The value of sum(r=1)^(10) r. (""^(n)C(r))/(""^(n)C(r-1) is equal to

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  6. If P(n) denotes the product of the binomial coefficients in the expan...

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  7. If C(0), C(1), C(2), ..., C(n) denote the binomial cefficients in t...

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  8. If C(0), C(1), C(2), …. C(n) denote the coefficients in the expansion ...

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  9. Statement-1: sum(r =0)^(n) (r +1)""^(n)C(r) = (n +2) 2^(n-1) Stat...

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  10. 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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  11. 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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  12. 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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  13. The sum of the series .^(20)C(0)-.^(20)C(1)+ .^(20)C(2)-.^(20)C(3)+...

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

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

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

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

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

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

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

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