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(n+2).^(n)C(0)2^(n+1).^(n)C(1)2^(n)+n.^(...

`(n+2).^(n)C_(0)2^(n+1).^(n)C_(1)2^(n)+n.^(n)C_(2)2^(n -1)-"…."` is equal to

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(n+2)C_0(2^(n+1))-(n+1)C_1(2^(n))+(n)C_2(2^(n-1))-.... is equal to

The value of .^(n)C_(1)+.^(n+1)C_(2)+.^(n+2)C_(3)+"….."+.^(n+m-1)C_(m) is equal to

The sum of the series 1+(1)/(2)""^(n)C_(1)+(1)/(3)""^(n)C_(2)+…+(1)/(n+1)""^(n)C_(n) is equal to-

If S_(n) = (.^(n)C_(0))^(2) + (.^(n)C_(1))^(2) +... +(.^(n)C_(n))^(n) , then maximum value of [(S_(n+1))/(S_(n))] is "_____" . (where [*] denotes the greatest integer function)

.^(n)C_(r)+2.^(n)C_(r-1)+.^(n)C_(r-2)=.^(n+2)C_(r)(2lerlen) .

If "^(n)C_(0)-^(n)C_(1)+^(n)C_(2)-^(n)C_(3)+...+(-1)^(r )*^(n)C_(r )=28 , then n is equal to ……

Evaluate .^(n)C_(0).^(n)C_(2)+.^(n)C_(1).^(n)C_(3)+.^(n)C_(2).^(n)C_(4)+"...."+.^(n)C_(n-2).^(n)C_(n) .

Find the sum of the series .^(n)C_(0)+2.^(n)C_(1)x+3.^(n)C_(2)x^(2)+....+(n+1).^(n)C_(n)x^(n) and hence show that , .^(n)C_(0)+2.^(n)C_(1)x+3.^(n)C_(2)x^(2)+....+(n+1)^(n)C_(n)=(n+2)2^(n-1)

If (1+x)^(n)=^(n)C_(0)+^(n)C_(1)x+^(n)C_(2)x^(2)+…+^(n)C_(n)x^(n) , prove that, nC_(1)-2^(n)C_(2)+3^(n)C_(3)-…+(-1)^(n-1).n^(n)C_(n)=0 .

If (1+x)^(n)=^(n)C_(0)+^(n)C_(1)x+^(n)C_(2)x^(2)+…+^(n)C_(n)x^(n) , prove that, nC_(0) +2^(n)C_(1)+3^(n)C_(2)+…+(n+1)^(n)C_(n)=(n+2)*2^(n-1) .

CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. 1+1/3x+(1xx4)/(3xx6)x^2+(1xx4xx7)/(3xx6xx9)x^3+------ is equal to

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  2. The value of sum(r=1)^(15)(r2^r)/((r+2)!) is (a).((17)!-2^16)/((17)!) ...

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  3. (n+2).^(n)C(0)2^(n+1).^(n)C(1)2^(n)+n.^(n)C(2)2^(n -1)-"…." is equal t...

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  4. The value of underset(r=0)overset(20)sum(-1)^(r )(.^(50)C(r))/(r+2) is...

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  5. In the expansion of [(1+x)(1-x)]^(2), the coefficient of x^(n) will be

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  6. If a, b, c are in GP and a, x, b,y, c ar in AP. then prove that, 1...

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  7. Statement 1: ""^m Cr+ ""^m C(r-1)(""^nC1)+ ""^mC(r-2)(""^n C2)+....+ "...

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  8. 1+(1/4)+((1*3)/(4*8))+((1*4*7)/(4*8*12))+....=

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  9. If |x|<1,then 1+n((2x)/(1+x))+(n(n+1))/(2!)((2x)/(1+x))^2+...... is eq...

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  10. If a, b, c are in AP also in GP Then show that, a=b=c

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  11. The sum of the GP (x+y)/(x-y), 1, (x-y)/(x+y),.....

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  12. Statement 1: In the expansion of (1+x)^(41)(1-x+x^2)^(40), the coeffic...

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  13. The coefficient of x^(n) in (1+x+(x^(2))/(2!) + (x^(3))/(3!) +"….." + ...

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  14. Evaluate the following .^3C2

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  15. Evaluate .^5C2

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  16. The value of sum(r=0)^(10)r""^(10)C(r)3^(r)(-2)^(10-r) is (a) 20 (b) 1...

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  17. Find n if n P1=2

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  18. Evaluate .^5P2

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  19. The value of (.^(n)C(0))/(n)+(.^(n)C(1))/(n+1)+(.^(n)C(2))/(n+2)+"..."...

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  20. The value of .^(20)C(0)+.^(20)C(1)+.^(20)C(2)+.^(20)C(3)+.^(20)C(4)+.^...

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