If x=∑∞n=0an,y=∑∞n=0bn,z=∑∞n=0cn where a, b, c, are in AP
and |a| <1,|b|<1,|c|<1 then x,y,z are in
A
GP
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B
AP
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C
Arithmetic- Geometric progression
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D
H.P
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Solution
The correct option is D H.P x=∑∞n=0an=11−aora=1−1xy=∑∞n=0bn=11−borb=1−1yz=∑∞n=0cn=11−corc=1−1z
a,b,c are in A.P. →2b=a+c 2(1−1y)=1−1x+1−1y⇒2y=1x+1z⇒x,y,zareinH.P.