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

Find the sum :`1/2*""^(n)C_0+""^(n)C_1+2*""^(n)C_2+2^2*""^nC_3+...+2^(n-1)*""^(n)C_n`.

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A DAS GUPTA-Binomial Theorem for Positive Integrel Index-Exercise
  1. Find the sum : ""^(2n+1)C0+""^(2n+1)C1+""^(2n+1)C2+...+""^(2n+1)Cn.

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

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

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

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

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

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

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

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

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  10. 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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  11. 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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  12. 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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  13. 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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  14. The sum of the binomial coefficients in the expansion of (x^2+1/x)^n i...

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

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

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

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

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  19. Evaluate (""^3C3+""^4C3+""^5C3+...+""^nC3)xx(""^nC3+""^nC4+""^nC5+...+...

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  20. The value of ^n C1+^(n+1)C2+^(n+2)C3++^(n+m-1)Cm is equal to ^m+n C(n-...

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