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If a,b,c and d are any four consecutive ...

If a,b,c and d are any four consecutive
coefficients in the expansion of `(1 + x)^(n)` , then prove that
(i)` (a) /(a+ b) + (c)/(b+c) = (2b)/(b+c) `
(ii) ` ((b)/(b+c))^(2) gt (ac)/((a + b)(c + d)), "if " x gt 0 ` .

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A DAS GUPTA-Binomial Theorem for Positive Integrel Index-Exercise
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  2. If a,b,c and d are any four consecutive coefficients in the expansi...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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