Asked by Ruby
1. Why cant you use the formula of the infinite geometric series on 1/81 + 1/27 + 1/9 + 1/3 + .....
2. Using concepts of infinite geometric series, show that 0.9999 ..... = 1.
2. Using concepts of infinite geometric series, show that 0.9999 ..... = 1.
Answers
Answered by
Reiny
r = (1/27) รท (1/81)
= 3
so the series diverges, that is, the terms are getting larger.
Think about adding terms that keep getting larger.
Clearly the sum will get larger and larger and eventually become infinitely large.
That is why for the formula
Sum (infinite number of terms) = a/(1-r)
part of the definition will be |r| < 1
2.
let .99999.. = .9 + .09 + .009 + ....
so a = .9 , and r = .1
sum(all terms) = .9/(1-.1)
= .9/.9
= 1
= 3
so the series diverges, that is, the terms are getting larger.
Think about adding terms that keep getting larger.
Clearly the sum will get larger and larger and eventually become infinitely large.
That is why for the formula
Sum (infinite number of terms) = a/(1-r)
part of the definition will be |r| < 1
2.
let .99999.. = .9 + .09 + .009 + ....
so a = .9 , and r = .1
sum(all terms) = .9/(1-.1)
= .9/.9
= 1
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.