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If in any binomial expansion a, b, c and d be the 6th, 7th, 8th and 9th terms respectively, prove that `(b^2-ac)/(c^2-bd)=(4a)/(3c)`

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A DAS GUPTA-Binomial Theorem for Positive Integrel Index-Exercise
  1. Show that there wil be a term independent of x in the expansion of (x^...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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