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Show that the HM of (2n+1)Cr and (2n+1)...

Show that the HM of (2n+1)C_r and (2n+1)C_(r+1)` is (2n+1)/(n+1)` times of `(2n)C_r` Also show that `sum_(r=1)^(2n-1) (-1)^(r-1)*r/(2nC_r)=n/(n+1)`.

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A DAS GUPTA-Binomial Theorem for Positive Integrel Index-Exercise
  1. Show that the HM of (2n+1)Cr and (2n+1)C(r+1) is (2n+1)/(n+1) times ...

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  2. Determine the constant term in the expansion of (1+x+x^2+x^3)^10

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  3. If the fourth term in the expansion of (px+1/x)^n is 5/2, then (n,p)...

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  4. Show that there wil be a term independent of x in the expansion of (x^...

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  5. Find the term which does not contain irrational expression in the expa...

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  6. If in any binomial expansion a, b, c and d be the 6th, 7th, 8th and 9t...

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  7. The value of x in the expression (x+x^((log)(10)))^5 if third term in ...

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  8. Prove that the coefficient of the middle term in the expansion of (1+x...

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  9. In the expansion of (1 + x)^43 ,the co-efficients of (2r + 1)th and (r...

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

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

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

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

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

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

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

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

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

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

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

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