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If `n` is a positive integer, prove that `1-2n+(2n(2n-1))/(2!)-(2n(2n-1)(2n-2))/(3!)++(-1)^(n-1)(2n(2n-1)(n+2))/((n-1)!)=(-1)^(n+1)(2n)!//2(n !)^2dot`

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CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
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  2. Prove that (^n C0)/x-(^n C0)/(x+1)+(^n C1)/(x+2)-+(-1)^n(^n Cn)/(x+n)=...

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  3. If n is a positive integer, prove that 1-2n+(2n(2n-1))/(2!)-(2n(2n-1)(...

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  4. Given, sn=1+q+q^2+.....+q^n ,Sn=1+(q+1)/2+((q+1)/2)^2+...+((q+1)/2)^n...

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  5. The sum of 1+n(1-1/x)+(n(n+1))/(2!)(1-1/x)^2+oo will be a. x^n b. x^(-...

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  6. sum(k=1)^ook(1-1/n)^(k-1)=>? a.n(n-1) b. n(n+1) c. n^2 d. (n+1)^2

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  7. The coefficient of x^4 in the expansion of {sqrt(1+x^2)-x}^(-1) in asc...

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  8. 1+1/3x+(1xx4)/(3xx6)x^2+(1xx4xx7)/(3xx6xx9)x^3+------ is equal to a. x...

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

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

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

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

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

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

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

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

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  17. 1+(1/4)+((1*3)/(4*8))+((1*4*7)/(4*8*12))+....=

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

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

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

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