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`        if a1,a2,a3,......an  real and greater than are euals to 1.PT (1/1+a1)+(1/1+a2)+......+(1/1+an)is greater than are equals to 1/1+(nth root of a1a2a3....an).`
7 years ago

28 Points
```										Dear,
ans:- We know that A.M>G.M>HM
or AM>HM
Using the above relation we get
1/n∑(1/1+a1)>n/∑(1+a1)
or ∑(1/1+a1)>n²/(n+∑a1)
Let ∑(1/1+a1)=S
then we Have S>n²/(n+∑a1)....................(1)
Now using AM>GM we get
(1/n)∑a1>(∏a1)^(1/n)...........................(2)
From 1 & 2 we get
S>n²/(n+n(∏a1)^1/n)
or S>n/(1+(n th root of  a1a2a3......an)  (Proved)

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7 years ago
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