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Prove that [(n+1)//2]^n >(n !)dot...

Prove that `[(n+1)//2]^n >(n !)dot`

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CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. In a triangle A B C prove that a/(a+c)+b/(c+a)+c/(a+b)<2

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  2. Find the least value of secA+secB+secC in an acute angled triangle.

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  3. Prove that [(n+1)//2]^n >(n !)dot

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  4. If a1+a2+a3+......+an=1 AA ai > 0, i=1,2,3,......,n, then find the ma...

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  5. If a ,b ,c are positive, then prove that a//(b+c)+b//(c+a)+c//(a+b)geq...

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  6. If (log)(10)(x^3+y^3)-(log)(10)(x^2+y^2-x y)lt=2, and x ,y are positiv...

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  7. If log2(a+b)+log2(c+d)ge4 . Then the minimum value of the expression a...

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  8. If a+b+c=1, then prove that 8/(27a b c)>{1/a-1}{1/b-1}{1/c-1}> 8.

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  9. If a ,b , a n dc are distinct positive real numbers such that a+b+c=1,...

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  10. If a^2+b^2+c^2-ab-bc-ca=0 then, prove that a=b=c

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  11. Find the minimum value of 4sin^(2)x+4cos^(2)x .

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  12. Prove that (a b+x y)(a x+b y)>4a b x y(a , b ,x ,y >0)dot

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  13. The minimum value of the sum of real number a^-5,a^-4,3a^-3,1,a^8 and ...

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  14. If a1,a2,.....an are positive real number whose product is a fixed num...

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  15. If a,b,c,d are positive real number such that a+b+c+d=2 , then M=(a+b)...

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  16. A straight line through the vertex P of a triangle P Q R intersects th...

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  17. If alpha in (0,pi/2), then sqrt(x^2+x)+tan^2alpha/sqrt(x^2+x) is alw...

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  18. In triangle A B C , prove that cos e c A/2+cos e c B/2+cos e c C/2geq...

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  19. Prove that in A B C ,tanA+tanCgeq3sqrt(3,) where A , B , C are circle...

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  20. If a ,b , a n dc are distinct positive real numbers such that a+b+c=1,...

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