Quiz 10.2:
Question:
Determine if \( \sum \limits _{n=0} ^\infty \frac{(-3)^n}{4^{n+1}} \) converges or diverges. If it converges, give its sum.
Solution:
Convergent geometric series \( |r|=|\frac{-3}{4}|=\frac{3}{4}<1 \)
And it sums to \( \frac{\frac{1}{4}}{1-\frac{-3}{4}}=\frac{1}{7} \)