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Every number of an infinite geometric progression of positive terms is equal to n times the sum of the numbers that follow it. What is the common ratio of progression?

Every number of an infinite geometric progression of positive terms is equal to n times the sum of the numbers that follow it. What is the common ratio of progression? Correct Answer 1/(n + 1)

Calculation:

Let the geometric progression be a, ar, ar2, ....

⇒ a = n × (ar + ar2 + ......) 

⇒ ar + ar2 + ........ = ar/1- r      (a = n × (ar/1 - r)

⇒ nr = 1 - r

⇒ r = 1/(n + 1)

∴ The required result will be 1/(n + 1).

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