if the sum of the series 1+ 2/x + 4/x^2 + 8/x^3 +...... infinity is a finite number then (a) x (b) x1/2 (c) x-2 (d) x2

Question

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

Y RAJYALAKSHMI · Answer

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 · Answer

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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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

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

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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

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

2 Answers

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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