In Example 2, change all − signs to + in the series.

Data from Example 2

Find the sum of the infinite geometric series

Here, we see that a 4. 1 = We find r by dividing any term by the previous term, and we find that r = −1/8. We then find the sum by substituting in Eq. (19.7). This gives us

In Fig. 19.6, the terms of the series are shown in L₂ and the sums of the first n terms are shown in L₃. We can see that the sums are approaching 32/9 = 3.555. . . .

4 T 1 2 16 + 1 128 +