If S+a1+a2+a3++an ,a1 in R^+ for i=1ton...

If `S+a_1+a_2+a_3++a_n ,a_1 in R^+` for `i=1ton ,` then prove that `S/(S-a_1)+S/(S-a_2)++S/(S-a_n)geq(n^2)/(n-1),AAngeq2`

Topper's Solved these Questions

INEQUALITIES INVOLVING MEANS
CENGAGE PUBLICATION|Exercise Example 1|1 Videos
INEQUALITIES INVOLVING MEANS
CENGAGE PUBLICATION|Exercise Example 2|1 Videos
INEQUALITIES INVOLVING MEANS
CENGAGE PUBLICATION|Exercise Comprehension|2 Videos
INEQUALITIES AND MODULUS
CENGAGE PUBLICATION|Exercise Single correct Answer|21 Videos
INTEGRALS
CENGAGE PUBLICATION|Exercise All Questions|762 Videos

Similar Questions

Explore conceptually related problems

If S=a_1+a_2+......+a_n,a_i in R^+ for i=1 to n, then prove that S/(S-a_1)+S/(S-a_2)+......+S/(S-a_n) ge n^2/(n-1), AA n ge 2

If a_1. a_2 ....... a_n are positive and (n - 1) s = a_1 + a_2 +.....+a_n then prove that (a_1 + a_2 +....+a_n)^n ge (n^2 - n)^n (s - a_1) (s - a_2)........(s - a_n)

If the sequence a_1, a_2, a_3,....... a_n ,dot forms an A.P., then prove that a_1^2-a_2^2+a_3^2-a_4^2+.......+ a_(2n-1)^2 - a_(2n)^2=n/(2n-1)(a_1^2-a_(2n)^2)

If a_1,a_2,a3,...,a_n are in A.P then show that 1/(a_1a_2)+1/(a_2a_3)+1/(a_3a_4)+...+1/(a_(n-1)a_n)=(n-1)/(a_1a_n)

If a_1, a_2,a_3, ,a_n is an A.P. with common difference d , then prove that "tan"[tan^(-1)(d/(1+a_1a_2))+tan^(-1)(d/(1+a_2a_3))+......+tan^(-1)(d/(1+a_(n-1)a_n))]=((n-1)d)/(1+a_1a_n)

If a_1, a_2,...... ,a_n >0, then prove that (a_1)/(a_2)+(a_2)/(a_3)+(a_3)/(a_4)+.....+(a_(n-1))/(a_n)+(a_n)/(a_1)> n

If |a_1sinx+a_2sin2x++a_nsinn x|lt=|sinx| for x in R , then prove that |a_1+2a_2+3a_3+n a_n|lt=1

If a ,a_1, a_2, a_3, a_(2n),b are in A.P. and a ,g_1,g_2,g_3, ,g_(2n),b . are in G.P. and h s the H.M. of aa n db , then prove that (a_1+a_(2n))/(g_1g_(2n))+(a_2+a_(2n-1))/(g_1g_(2n-1))++(a_n+a_(n+1))/(g_ng_(n+1))=(2n)/h

If the coefficients of four consecutive terms in the expansion of (1+x)^n are a_1,a_2,a_3 and a_4 respectively. then prove that a_1/(a_1+a_2)+a_3/(a_3+a_4)=2a_2/(a_2+a_3).

a_1, a_2, a_3, in R-{0} and a_1+a_2cos2x+a_3sin^2x=0 for all x in R , then

CENGAGE PUBLICATION-INEQUALITIES INVOLVING MEANS -Illustration

about to only mathematics
Text Solution
|
If a+b+c=1, then prove that 8/(27a b c)>{1/a-1}{1/b-1}{1/c-1}> 8.
Text Solution
|
If y z+z x+x y=12 ,w h e r ex ,y ,z are positive values, find the grea...
Text Solution
|
If a ,b ,c are positive, then prove that a//(b+c)+b//(c+a)+c//(a+b)geq...
Text Solution
|
Prove that 2^n >1+nsqrt(2^(n-1)),AAn >2 where n is a positive integer.
Text Solution
|
If S+a1+a2+a3++an ,a1 in R^+ for i=1ton , then prove that S/(S-a1)+S/...
Text Solution
|
If a1+a2+a3+......+an=1 AA ai > 0, i=1,2,3,......,n, then find the ma...
Text Solution
|
If a , b , c , are positive real numbers, then prove that (2004, 4M) {...
Text Solution
|
Prove that (sec^4alpha)/(tan^2beta)+(sec^4beta)/(tan^2alpha)ge8. If ea...
Text Solution
|
Prove that [(x^2+y^2+z^2)/(x+y+z)]^(x+y+z)> x^x y^y z^z >[(x+y+z)/3]^(...
Text Solution
|
Prove that 1^1xx2^2xx3^3xxxxu nlt=[(2n+1)//3]n(n+1)//2,n in Ndot
Text Solution
|
Find the greatest value of x^2 y^3, where x and y lie in the first qua...
Text Solution
|
Find the maximum value of (7-x)^4(2+x)^5w h e nx lies between -2a n d7...
Text Solution
|
Find the maximum value of xyz when (x)/(1)+(y^2)/(4)+(z^3)/(27)=1, whe...
Text Solution
|
If a ,b >0 such that a^3+b^3=2, then show that a+blt=2.
Text Solution
|
If m >1,n in N show that 1m+2m+2^(2m)+2^(3m)++2^(n m-m)> n^(i-m)(2^n-...
Text Solution
|
Prove that in an acute angled triangle ABC , sec A+sec B +sec Cge 6.
Text Solution
|
Prove that (b^2+c^2)/(b+c)+(c^2+a^2)/(c+a)+(a^2+b^2)/(a+b)> a+b+c
Text Solution
|
Prove that (a^8+b^8+c^8)/(a^3b^3c^3)>1/a+1/b+1/c
Text Solution
|
If a ,b ,a n dc are positive and a+b+c=6, show that (a+1//b)2+(b+1//c)...
Text Solution
|