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Prove that 1^1xx2^2xx3^3xxxxn^nlt=[(2n+1...

Prove that `1^1xx2^2xx3^3xxxxn^nlt=[(2n+1)//3]^(n(n+1)//2),n in Ndot`

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CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. If a ,b ,a n dc are positive and a+b+c=6, show that (a+1//b)^2+(b+1/...

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  2. Prove that [(x^2+y^2+z^2)/(x+y+z)]^(x+y+z)> x^x y^y z^z >[(x+y+z)/3]^(...

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  3. Prove that 1^1xx2^2xx3^3xxxxn^nlt=[(2n+1)//3]^(n(n+1)//2),n in Ndot

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  4. Prove that 2/(b+c)+2/(c+a)+2/(a+b)lt1/a+1/b+1/c ,where a ,b ,c>0.

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  5. The minimum value of 2^sinx+2^cosx

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  6. In how many parts an integer N>=5 should be dissected so that the pro...

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  7. In triangle ABC internal angle bisector AI,BI and CI are produced to m...

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  8. The minimum value of (x^4+y^4+z^2)/(x y z) for positive real numbers x...

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  9. If x+y+z=1a n dx ,y ,z are positive, then show that (x+1/x)^2+(y+1/y)^...

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  10. The least value of 6tan^2varphi+54cot^2varphi+18 is (I)54 when A.M.g...

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  11. A rod of fixed length k slides along the coordinates axes, If it meet...

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  12. If y=3^(x-1)+3^(-x-1) , then the least value of y is (a)2 (b)6 (c...

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  13. If a b^2c^3, a^2b^3c^4,a^3b^4c^5 are in A.P. (a ,b ,c >0), then the mi...

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  14. If the product of n positive numbers is n^n , then their sum is (a) a ...

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  15. Minimum value of (b+c)//a+(c+a)//b+(a+b)//c (for real positive number...

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  16. Prove that px^(q - r) qx^(r - p) + rx^(p - q) gt p + q + r where p,q,...

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  17. Given are positive rational numbers a ,b , c such that a+b+c=1, then p...

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  18. Prove that [(a^2+b^2)/(a+b)]^(a+b)> a^a b^b >{(a+b)/2}^(a+b)dot

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  19. Prove that a^p b^ q <((a p+b q)/(p+q))^(p+q)dot

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  20. Let x1, x2, ,xn be positive real numbers and we define S=x1+x2++xndot...

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