Question: 3. (5 points) Consider the infinite repeating decimal .999999.... We can write this number as an infinite series .9+.09+.009+.0009 +00009 +.000009.. (a) This is

3. (5 points) Consider the infinite repeating decimal .999999.... We can write

3. (5 points) Consider the infinite repeating decimal .999999.... We can write this number as an infinite series .9+.09+.009+.0009 +00009 +.000009.. (a) This is a multiple of a geometric series so can be written as .... a +ar+ar + ar + ar +... = a(1+r+p +p +r +...). What numbers a and r give the series .9+.09+.009+.0009+.00009+.000009...? (b) Use the formula for the sum of a geometric series to compute the sum. (c) Is this what you expected? Explain why or why not.

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