Mathematics

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

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
Correct Answer: Option A
Explanation

(a=1, r=frac{9}{10}\
S_n = frac{a}{1-r}\
S_n = frac{1}{1-frac{9}{10}}\
=1div frac{1}{10}\
=1times frac{10}{1}\
10)