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If a,b,c are in GP Then prove that, lo...

If a,b,c are in GP Then prove that, `loga ,logb , logc` are in AP.

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CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. Second term of a GP is 6 and its 5th term is 9th time of its 3rd term....

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  2. The 4th term and the 9th term of a GP is 54 and 13122 respectively. Fi...

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  3. If a,b,c are in GP Then prove that, loga ,logb , logc are in AP.

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  4. If the coefficient of x^(7)in [ax^(2) + (1/bx)]^(11) equals the coeffi...

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  5. If the binomial coefficient of the (2r+4)^(th) term and (r-2)^(th) ter...

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  6. If the coefficients of the rth, (r+1)t h ,(r+2)t h terms is the expan...

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  7. If the three consecutive coefficients in the expansion of (1+x)^n are...

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  8. The expression (sqrt(2x^2+1)+sqrt(2x^2-1))^6 + (2/(sqrt(2x^2+1)+sqrt(2...

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  9. Least positive integer just greater than (1+0.00002)^(50000) is "".

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  10. If U(n) = (sqrt(3) + 1)^(2n) +(sqrt(3) - 1)^(2n), then prove that ...

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  11. Prove that the coefficient of x^(n) in the expansion of (1)/((1-x)(1-2...

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  12. The value of (30,0)(30,10)-(30,1)(30,11)+(30,2)(30,12)-........+(30,20...

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  13. If a, b, c are in AP, a, x, b are in GP , where as b, y and c also in...

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  14. Prove that 1/(m !).^n C0+n/((m+1)!).^n C1+(n(n-1))/((m+2)!).^n C2+.......

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  15. If n=12 m(m in N), prove that .^n C0-(.^n C2)/((2+sqrt(3))^2)+(.^n C...

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  16. Prove that in the expansion of (1+x)^(n) (1+y)^(n) (1+z)^(n), the sum ...

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  17. Prove that .^100 C0^(100)C2+^(100)C2^(100)C4+^(100)C4^(100)C6++^(100)C...

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  18. Prove that sum(r=1)^(m-1)(2r^2-r(m-2)+1)/((m-r)^m Cr)=m-1/mdot

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  19. Find the coefficients of x^(50) in the expression (1+x)^(1000)+x(1+x)^...

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  20. If a, b, c are in GP and a, x, b, y are in AP Then prove that, a/x + ...

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