Question

How do you find the sum of the infinite geometric series 215 - 86 + 34.4 - 13.76 + ...?

Answer 1

Use the formula `a+ar+ar^{2}+ar^{3}+cdots=a/(1-r)` (for `|r| < 1`) to get `1075/7 approx 153.6`.

Explanation:

The series `215-86+34.4-13.76+cdots` is geometric with first term `a=215` and common ratio `r=-86/215=-2/5=-0.4`.

The formula above therefore gives `a/(1-r)=215/(1+2/5)=215/(7/5)=(215 * 5)/7=1075/7 approx 153.6`.