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If x=Sigma(n=0)^(oo) a^n,y=Sigma(n=0)^(...

If `x=Sigma_(n=0)^(oo) a^n,y=Sigma_(n=0)^(oo) b^n,z=Sigma_(n=0)^(oo) c^n` where a, b,and c are in A.P and `|a|lt 1 ,|b|lt 1 and |c|1 `then prove that x,y and z are in H.P

Text Solution

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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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