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If (1+x)^n=C0+C1x+C2x^2+.......+Cn x^n ,...

If `(1+x)^n=C_0+C_1x+C_2x^2+.......+C_n x^n` , then show that the sum of the products of the coefficients taken two at a time, represented by `sumsum_(0lt=iltjlt=n) ``""^nc_i` `""^n c_j` is equal to `2^(2n-1)-((2n)!)/ (2(n !)^2)`

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CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
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  2. If sum(r=0)^(n) (r)/(""^(n)C(r))= sum(r=0)^(n) (n^(2)-3n+3)/(2.""^(n)C...

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  3. If (1+x)^n=C0+C1x+C2x^2+.......+Cn x^n , then show that the sum of the...

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  4. If sum(r=0)^(n){a(r)(x-alpha+2)^(r)-b(r)(alpha-x-1)^(r)}=0, then

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  5. Let a=(2^(1//401)-1) and for each ngeq2,l e tbn=^n C1+^n C2dota+^n C3...

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  6. Prove that underset(r=0)overset(n)sum.^(n)C(r)(-1)^(r)[i^(r)+i^(2r)+i^...

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  7. The coefficients of x^n in (1+x/(1!)+x^2/(2!)+……+x^n/(n!))^2 is

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  8. If the first and third term is 2 and 8 respectively. Find its secon...

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

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

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

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

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

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

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  16. 1+1/3x+(1xx4)/(3xx6)x^2+(1xx4xx7)/(3xx6xx9)x^3+------ is equal to

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

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

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

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