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Question

If the sum of an infinite G.P, whose first term is 9, is x, then x belongs to


  1. None of these


Solution

The correct option is A

In an infinite G.P. , for the sum to be finite, the common ratio r should lie between -1 and 1.

Or     -1 < r < 1

91r = x  [ Sum of the G.P.]

x = 91r

r =  x9x

-1 <  r  < 1

-1 < x9x  < 1

We will split the inequality as 

x9x >  - 1          and          x9x <  1

x - 9 > - x                                and           x - 9 < x

2x > 9                                      and            -9  < 0

x > 92 and -9 is less than zero for all values of x. So we don't have to use this part, because it does not impose any

condition. 

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