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If n is a positive integer, prove that 1...

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 PUBLICATION-BINOMIAL THEOREM-All Questions
  1. If the first and third term is 2 and 8 respectively. Find its secon...

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  2. Find the next two terms of the series 2,-6,18,-54,.....

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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. Find the third term from the end term of the GP.2/27, 2/9, 2/8,.........

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  5. 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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  6. The sum of 1+n(1-1/x)+(n(n+1))/(2!)(1-1/x)^2+.....oo

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  7. sum(k=1)^ook(1-1/n)^(k-1) =?

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  8. The coefficient of x in the expansion of {sqrt(1+x^2)-x}^(-1) in ascen...

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  9. 1+1/3x+(1xx4)/(3xx6)x^2+(1xx4xx7)/(3xx6xx9)x^3+------ is equal to

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

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

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

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

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

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  16. 1+(1/4)+((1*3)/(4*8))+((1*4*7)/(4*8*12))+....=

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

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

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

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

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