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# 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

Grade:12th pass

## 2 Answers

Y RAJYALAKSHMI
45 Points
7 years ago
1+ 2/x + 4/x^2 + 8/x^3 +......  is sum of terms in GP where r = 2/x.
The sum is finite if |r| |2/x| |x| > 2 => x 2

Ans: x 2
SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
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

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