Calculate the sum of the geometric series 1 - 1/5 + 1/5^2 - 1/5^3 + .... Express your answer as a common fraction.

This is a geometric series with first term = 1 and common ratio = -1/5.

Using the formula for an infinite geometric series with a common ration -1 < r < 1:

Sum = 1 / ( 1 - 1/5) = 1 / (4/5) = 5/4.

Sum == 1 / [1 - ( - 1/5)] ==1 / [1 + 1/5] ==1 / [6/5] ==5/6 [geno3141 made a small typo]