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Given positive integers r>1,n> 2, n bei...

Given positive integers `r>1,n> 2, n` being even and the coefficient of `(3r)th` term and `(r+ 2)th` term in the expansion of `(1 +x)^(2n)` are equal; find r

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A DAS GUPTA-Binomial Theorem for Positive Integrel Index-Exercise
  1. Prove that in the expansion of (1+x)^(2n), the coefficient of x^n is d...

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  2. The coefficient of 5th, 6th and 7th terms in the expansion of (1+x)^n ...

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  3. Given positive integers r>1,n> 2, n being even and the coefficient of...

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  4. If the coefficients of three consecutive terms in the expansion of (1 ...

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  5. If a,b,c be the three consecutive coefficients in the expansion of a p...

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  6. If a,b,c and d are any four consecutive coefficients in the expansi...

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  7. If a,b,c and d are any four consecutive coefficients in the expansi...

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  8. If the four consecutive coefficients in any binomial expansion be a, b...

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  9. Let (1+x^2)^2*(1+x)^n=sum(k=0)^(n+4)ak*x^k If a1, a2 and a3 are iun ...

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  10. If n be a positive integer then prove that the integral part P of (5+2...

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  11. If (9+4sqrt5)^n=p+beta where n and p are positive integers and beta is...

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  12. Integer just greater tehn (sqrt(3)+1)^(2n) is necessarily divisible by...

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

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  14. If x=1//3, find the greatest tem in the expansion of (1+4x)^8dot

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  15. Find the numerically greatest term in the expansion of (3-2x)^9 when x...

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  16. Find the value of the greatest term in the expansion of sqrt3(1+frac{1...

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  17. In the expansion of (x+a)^15, if the eleventh term is the geometric me...

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  18. In the expansion of (frac{3}{2}+frac{x}{3})^n when x=frac{1}{2} , it i...

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

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

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