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Asked by buttercup | 9th Mar, 2012, 02:06: PM

Expert Answer:

here An = (An-1 + Hn-1)/2 , Hn = 2An-1.Hn-1/(An-1 + Hn-1) , Gn = sqroot(An-1.Hn-1)
 
On multiplying the first 2 equations we get  An.Hn = An-1.Hn-1 ,
So Gn+1 = G, Thus G1 = G2 = G3 =...........
 
Also it can be seen that An > Gn > Hn ,
Now,
An+1 is the arithmetic mean of An and Hn , Thus An > An+1 ,
 
So An is in order i.e. A1 > A2 > A3 > ......
 
Similarly
 
Hn is in order H1

Answered by  | 12th Mar, 2012, 11:40: AM

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