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#### mathworker

##### Active member

- May 31, 2013

- 118

**IMO-2012:**

let \(\displaystyle a_2,a_3,.....,a_n\) be positive real numbers that satisfy a

_{2.}a

_{3}......a

_{n}=1 .Prove that,

\(\displaystyle (a_2+1)^2.(a_3+1)^3.......(a_n+1)^n>n^n\)

hint:

Use A.M>G.M