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Let a,b,c be in A.P. and |a|lt1, |b|lt1|...

Let a,b,c be in A.P. and `|a|lt1,` `|b|lt1|,` `|c|lt1`. if `x=1+a+a^(2)+ . . . ."to "oo,` `y=1+b+b^(2)+ . . . ."to "ooand,z=1+c+c^(2)+ . . . "to "oo`, then `x, `y, `z` are in

A

AP

B

GP

C

HP

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
c
Given , `x = 1 +a+a^(2) + … oo = 1/(1-a)`
` y = 1+b+b^(2) +…oo = 1/(1-c)`
and ` z= 1+c+c^(2) +…oo 1/(1-c)`
Now, a,b,c,are in AP.
` rArr 1- a, 1-b , 1-c ` are in AP.
`rArr 1/(1-a),1/(1-b),1/(1-c)` ` are in HP.
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