if the sum of the series 1+ 2/x + 4/x^2 + 8/x^3 +...... infinity is a finite number then(a) x(b) x>1/2(c) x>-2(d) x2

Hello student,
Please find the answer to your question below
The given series can be written as
1+ 2/x + 4/x^2 + 8/x^3 +......=(1-(2/x))^-1
where r=2/x
For a series to be finite |r|<1 so |2/x|<1
So |x|>2