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.