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The real number 0.9 can be written as an infinite series as shown below: 9 9 9 0.9 = + + + 10 100

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The real number 0.9 can be written as an infinite series as shown below: 9 9 9 0.9 = + + + 10 100 1000 (a) Write the infinite series in sigma notation and use the formula for the sum of a infinite geometric series to find the sum. (b) Write the exact value of the infinite sum (not as a repeating decimal).

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