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If x=sum(n=0)^ooa^n , y=sum(n=0)^oob^n ,...

If `x=sum_(n=0)^ooa^n , y=sum_(n=0)^oob^n , z=sum_(n=0)^ooc^n , w h e r e ra ,b ,a n dc` are in A.P. and `|a|<,|b|<1,a n d|c|<1,` then prove that `x ,ya n dz` are in H.P.

Text Solution

Verified by Experts

Here, `x=1/(1-a),y=1/(1-b),z=1/(1-c)`
Since a,b,c are in A.P. so
1-a,1-b,1-c are in A.P.
`rArr1/(1-a),1/(1-b),1/(1-c)` are in H.P.
`rArrx,y,z` are in H.P.
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