Question

What is the sum of the first five terms in this series?
6 - 6/3 + 6/9 - 6/27 + . . .?

Answer 1

4 14/27

Explanation:

The first five terms

6

-6/3

6/9

-6/27

+6/81

The first thing to do is change all the fractions denominators to 81.

Sum = 6*81/81 - 6(27)/81 + 6*9/81 - 6*3/81 + 6/81

Now add

Sum = 366/81

Sum = 4 14/27

Sum = 4.5185

Note the first term. It has been multiplied by 6*81/81. The 81 over 81 does not change the value of anything 6 * 81/81 is still 6. It just makes it easier to combine with the other members of the series.