Question

# If the sum of an infinite G.P, whose first term is 9, is x, then x belongs to 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 91−r = x  [ Sum of the G.P.] ⇒ x = 91−r ⇒ r =  x−9x -1 <  r  < 1 ⇒ -1 < x−9x  < 1 We will split the inequality as  x−9x >  - 1          and          x−9x <  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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