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Find the sum : ""^(2n+1)C0+""^(2n+1)C1+"...

Find the sum : `""^(2n+1)C_0+""^(2n+1)C_1+""^(2n+1)C_2+...+""^(2n+1)C_n`.

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The standard deviation of the data: x : 1 a a^2 ... a^n f: ^n C_0 ^n C_1 ^n C_2 ... ^n C_n is (a)((1+a^2)/2)^n-((1+a^2)/2)^n (b) ((1+a^2)/2)^(2n)-((1+a^2)/2)^(2n) (c) ((1+a^)/2)^(2n)-((1+a^2)/2)^n (d) none of these

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A DAS GUPTA-Binomial Theorem for Positive Integrel Index-Exercise
  1. In the expansion of (frac{3}{2}+frac{x}{3})^n when x=frac{1}{2} , it i...

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  2. Prove that the greatest coefficient in the expansion of (1+x)^(2n) is...

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  3. Find the sum : ""^(2n+1)C0+""^(2n+1)C1+""^(2n+1)C2+...+""^(2n+1)Cn.

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  4. The sum of the series 1/(1!(n-1)!)+1/(3!(n-3)!)+1/(5!(n-5)!)+…..+1/((n...

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  5. Find the sum :1/2*""^(n)C0+""^(n)C1+2*""^(n)C2+2^2*""^nC3+...+2^(n-1)*...

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  6. Prove that : (1+""^nC1+""^nC2+""^nC3+...+""^nCn)^2=1+""^(2n)C1+""^(2n)...

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  7. If t0,t1, t2,...,tn are the terms in the expansion of (x+a)^n then pro...

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  8. If (1+x-x^2)^10/(1+x^2)=a0+a1x+a2x^2+...+anx^n+… then find a0+a1+a2+….

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  9. If (1+x-x^2)^10/(1+x^2)=a0+a1x+a2x^2+...+anx^n+… then find a0-a1+a2......

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  10. If (1+x-x^2)^10/(1+x^2)=a0+a1x+a2x^2+...+anx^n+… then find a0+a2+a4+…

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  11. If (1+x-x^2)^10/(1+x^2)=a0+a1x+a2x^2+...+anx^n+… then find a1+a3+a5+…

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  12. If (1+x-x^2)^n/(1+x^2)=a0+a1x+a2x^2+...+a(2n)x^(2n) then find a0+a1+a2...

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  13. If (1+x-x^2)^n/(1+x^2)=a0+a1x+a2x^2+...+a(2n)x^(2n) then find a0-a1+a2...

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  14. If (1+2x-x^2)^n/(1+x^2)=a0+a1x+a2x^2+...+a(2n)x^(2n) then find a0+a2+a...

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  15. If (1+x-x^2)^n/(1+x^2)=a0+a1x+a2x^2+...+a(2n)x^(2n) then find a1+a3+a5...

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  16. The sum of the binomial coefficients in the expansion of (x^2+1/x)^n i...

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  17. The exponent of a binomial exceeds that of another by 3. the sum of th...

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  18. Find the coefficient of x^3 in the expansion of 1+(1+x)+(1+x)^2+(1+x)^...

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  19. Find the coefficients of x^(50) in the expression (1+x)^(1000)+2x(1+x)...

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  20. (b) Find the value of sum(r=m)^n .^rCm,n>m

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