Algebra

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.

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asked by Ruby
  1. r = (1/27) ÷ (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

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    posted by Reiny

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