Evaluate 1+1/3+1/9+1/27

Problem

1+1/3+1/9+1/27

Solution

1. Identify the expression as a finite geometric series where the first term a=1 and the common ratio r=1/3

2. Find a common denominator for all terms, which is 27

3. Rewrite each fraction using the common denominator: 1=27/27 1/3=9/27 and 1/9=3/27

4. Sum the numerators over the common denominator: 27 + 9 + 3 + 1 = 40$.

Final Answer

1+1/3+1/9+1/27=40/27

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