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If C(r) stands for .^(r)C(r), then the s...

If `C_(r)` stands for `.^(r)C_(r)`, then the sum of the first `(n+1)` terms o the series `aC_(0)-(a+d)C_(1)+C_(1)+(a+2d)C_(2)-(a+3d)C_(3)+ . . .` is equal to_____

A

`(a)/(2^(n))`

B

`na`

C

0

D

none of these

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The correct Answer is:
c
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OBJECTIVE RD SHARMA ENGLISH-BINOMIAL THEOREM AND ITS APPLCIATIONS -Exercise
  1. The coefficient of x^(-10) in (x^2-1/x^3)^10, is

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  2. If the coefficients of rth, (r+1)t h ,a n d(r+2)t h terms in the expan...

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

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  4. If (1 + x + x^2)^n = (C0 + C1x + C2 x^2 + ............) then the value...

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  5. If the coefficients of 2nd, 3rd and the 4th terms in the expansion of ...

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  6. If the coefficient of 2nd, 3rd and 4th terms in the expansion of (1...

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  7. If the 6th term in the expansion of(1/(x^(8/3))+x^2(log)(10)x)^8 is 56...

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  8. Find the term in(3sqrt(((a)/(sqrt(b))) + (sqrt((b)/ ^3sqrt(a))))^(21) ...

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  9. If the coefficients of 2nd, 3rd and 4th terms in the expansion of (1+...

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  10. Find the coefficient of x^4 in the expansion of (1+x+x^2+x^3)^(11)dot

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  11. If (1 + x - 2 x^(2))^(6) = 1 + C(1) x + C(2) x^(2) + C(3) x^(3) + …+ C...

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  12. If the coefficient of the middle of term in the expansion of (1+x)^(2n...

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  13. If a1,a2, a3, a4 be the coefficient of four consecutive terms in the e...

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

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  15. If (1-x+x^2)^n=a0+a1x+a2x^2+ .........+a(2n)x^(2n),\ find the value o...

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  16. The coefficient of x^m in (1+x)^m +(1+m)^(m+1) +...+(1+x)^n ,m≤n is

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  17. the coefficient of x^(7) in (ax - b^(-1) x^(-2))^(11) is

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  18. Find the coefficient of x^5 in the expansion of (1+x^2)^5(1+x)^4.

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  19. Find the greatest term in the expansion of sqrt(3)(1+1/(sqrt(3)))^(20)...

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  20. If T0,T1, T2, ,Tn represent the terms in the expansion of (x+a)^n , t...

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