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(n+2)C0(2^(n+1))-(n+1)C1(2^(n))+(n)C2(2^...

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

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If the value of (n + 2) . ""^(n)C_(0) *2^(n+1) - (n+1) * ""^(n)C_(1)*2^(n) + n* ""^(n)C_(2) * 2^(n-1) -... is equal to k(n +1) , the value of k is .

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

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

If C_(0) , C_(1) , C_(2) ,…, C_(n) are coefficients in the binomial expansion of (1 + x)^(n) and n is even , then C_(0)^(2)-C_(1)^(2)+C_(2)^(2)+C_(3)^(2)+...+ (-1)^(n)C_(n)""^(2) is equal to .

If C_(0),C_(1),C_(2),…,C_(n) are the binomial coefficients in the expansion of (1+x)^(n)*n being even, then C_(0)+(C_(0)+C_(1))+(C_(0)+C_(1)+C_(2))+….+(C_(0)+C_(1)+C_(2)+…+C_(n-1)) is equal to :

(1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+….+C_(n)x^(n) then C_(0)C_(2)+C_(1)C_(3)+C_(2)C_(4)+…..+C_(n-2)C_(n) is equal to :

If n in N, then sum_(r=0)^(n) (-1)^(n) (""^(n)C_(r))/(""^(r+2)C_(r)) is equal to .

If C_(0),C_(1),C_(2),C_(3), . . .,C_(n) be binomial coefficients in the expansion of (1+x)^(n) , then Q. The value of the expression C_(0)-2C_(1)+3C_(2)-. . . .+(-1)^(n)(n+1)C_(n) is equal to

If (1 + x)^(n) = C_(0) + C_(1)x + C_(2) x^(2) + …+ C_(n) x^(n) , then for n odd, C_(1)^(2) + C_(3)^(2) + C_(5)^(2) +....+ C_(n)^(2) is equal to

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

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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)C0(2^(n+1))-(n+1)C1(2^(n))+(n)C2(2^(n-1))-.... is equal to

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  4. The value of sum(r=0)^(50)(-1)^r((50)Cr)/(r+2) is equal to a . 1/(50x...

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

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  6. Statement : The sum of coefficient in the expansion of (3^(-x//4)+3^(5...

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  7. Let n be a positive integer and k be a whole number, klt=2ndot Statem...

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  8. Statement 1: sum sum(0le ilt j le n)(i/ (.^n ci)+j/(.^ncj)) is equal t...

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  9. Statement 1: ^m Cr+^m C(r-1)(^nC1)+^mC(r-2)(^n C2)+....+^n Cr=0 , if m...

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  10. 1+(1/4)+((1*3)/(4*8))+((1*4*7)/(4*8*12))+....=

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

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  12. Statement 1: If p is a prime number (p!=2), then [(2+sqrt(5))^p]-2^(p+...

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  13. Statement 1: The total number of dissimilar terms in the expansion of ...

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

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  15. Statement 1: The coefficient of x^n in (1+x+(x^2)/(2!)+(x^3)/(3!)++(x^...

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  16. Evaluate 3C2

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  17. Evaluate 5C2

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  18. Find underset(r=0) overset(10)sumr^ (10)C(r).3^(r).(-2)^(10-r)

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  19. Find n if nP1=2

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  20. Evaluate 5P2

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