10.4, #1. This is a geometric series with a = 2 and r = 1/2, its sum is 4. 10.4, #2. This is a geometric series with a = 1 and r = −1/2, its sum is 2/3. 10.4, #3. This is not a geometric series: the (n + 1)-st term comes from the n-th term by multiplying by n/(n + 1) instead of a constant factor. 10.4, #5 and #11. This is a geometric series with a = 1 and r = −x. It converges to

\frac{1}{1 + x} for |x| < 1.

10.4, #12. The series in #7 is geometric converging to \frac{y^{2}}{1 − y} for |y| < 1.

10.4, #13. The series in #8 is geometric converging to \frac{1}{1 − y^{2}} for |y| < 1.