Find to infinity, the sum of the sequence \(1, \frac{9}{10}, \left(\frac{9}{10}\right)^2, \left(\frac{9}{10}\right)^3,.....\)

  • A 10
  • B 9
  • C 10/9
  • D 9/10
jamb 2009mathematics

The correct answer is A. 10

The given sequence is a geometric sequence with first term a = 1 and common ratio r = 9/10. The sum of an infinite geometric sequence with first term a and common ratio r, where |r| < 1, is given by the formula:

S = a/(1-r)

Substituting the values for a and r, we get:

S = 1/(1-9/10)

= 1/(1/10)

= 10

So, the sum of the given infinite geometric sequence is 10.

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