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Which of the following geometric series is a representation of the repeating decimal 0.999999…?

2 Answers

5 votes

Answer:

A & C.

.99+.0099+.000099

&

.9+.09+.009

Explanation:

User MissingNumber
by
8.0k points
4 votes

Answer:

9(1/10) [1+(1/10)+(1/10)^2+(1/10)^3+.....]

Explanation:

0.99999...= 9(1/10) + 9(1/10)^2+9(1/10)^3+9(1/10)^4+.....

taking 9(1/10) common,

=9(1/10) [1+(1/10)+(1/10)^2+(1/10)^3+.....]

therefore, this is the required geometric series.

  • the sum of the infinite series: 1+r+r^2+r^3+r^4+r^5+r^6....

is,
(1)/(1-r)

  • the series inside the square brackets are infinite geometric progression series.

so the whole sum = 9(1/10)[
(1)/(1-(1)/(10) )]

=9(1/10)[10/9]

=1

User Ignat Galkin
by
8.5k points