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

If `(9+4sqrt5)^n=p+beta` where n and p are positive integers and `beta` is a positive proper fraction, prove that `(1-beta)(p+beta)=1`.

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A DAS GUPTA-Binomial Theorem for Positive Integrel Index-Exercise
  1. 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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  2. If n be a positive integer then prove that the integral part P of (5+2...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. If (1+x-x^2)^10/(1+x^2)=a0+a1x+a2x^2+...+anx^n+… then find a0+a1+a2+….

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  18. If (1+x-x^2)^10/(1+x^2)=a0+a1x+a2x^2+...+anx^n+… then find a0-a1+a2......

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  19. If (1+x-x^2)^10/(1+x^2)=a0+a1x+a2x^2+...+anx^n+… then find a0+a2+a4+…

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  20. If (1+x-x^2)^10/(1+x^2)=a0+a1x+a2x^2+...+anx^n+… then find a1+a3+a5+…

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