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Find the value of sum(p=1)^n(sum(m=p)^n^...

Find the value of `sum_(p=1)^n(sum_(m=p)^n^n C_m^m C_p)dot` And hence, find the value of `(lim)_(nvecoo)1/(3^n)sum_(p=1)^n(sum_(m=p)^n^n C_m^m C_p)dot`

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A DAS GUPTA-Binomial Theorem for Positive Integrel Index-Exercise
  1. Prove that (""^nC1)/(""^nC0)+2*(""^nC2)/(""^nC1)+3*(""^nC3)/(""^nC2)+....

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

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  3. Find the value of sum(p=1)^n(sum(m=p)^n^n Cm^m Cp)dot And hence, find ...

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  4. The value of ^(2n+1)C0^2+^(2n+1)C1^2+^(2n+1)C2^2+....+^(2n+1)Cn^2 is e...

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  5. Find the sum sumsum(0lt=i<jlt=n)^n Ci^n Cj

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  6. If (1 + x + x^(2) + x^(3))^(n) = a(0) + a(1)x + a(2)x^(2)+"……….."a(3n)...

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  7. The coefficient of a^4b^5 in the expansion of (a+b)^9 is .

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  8. The coefficient in the third term of the expansion of (x^2-1/4)^n when...

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  9. Which is larger : (99^(50)+100^(50)) or (101)^(50).

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  10. The sum of the coefficeints of the polynominal (1 + x - 3x^(2))^(2163)...

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  11. The sum of the numerical coefficients in the expansion of (2x+3y)^10 i...

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  12. If the fifth term of the expansion (a^(2//3)+a^(-1))^n does not contai...

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  13. The sum of the rational terms in the expansion of (sqrt(2)+ root(5...

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  14. Write the middle term in the expansion of (x+1/x)^(10)dot

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  15. If the coefficients of 2nd, 3rd and 4th terms in the expansion of(1+x)...

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  16. If x^r occurs in the expansion of (x+1/x)^n then its coefficient is .

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  17. If the sum of the coefficients in the expansion of (a+b)^n is 4096, th...

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  18. The number of terms in the expansion of (1+x^(1/5))^55 which are free ...

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  19. If n is even then the coefficient of x in the expansion of (1+x)^n*(1-...

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  20. The sum of ""^21C0+""^21C1+""^21C2+...+""^21C10 is equal to .

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