CPM Homework Help : PC Problem 8-123

Find the sum of the following infinite geometric series. If the answer is “∞,” explain why. Homework Help ✎
3. a + 0.9a + 0.81a + 0.729a + …
4. 1 + 1.1 + 1.21 + 1.331 + …

Answer (a):

$a_n=\left(\frac{1}{2}\right)^{n-1} \ \ \text{Sum}=\frac{1}{1-\frac{1}{2}}=\frac{1}{\frac{1}{2}}=2$

Hint (b):

$a_n=16\left(\frac{1}{4}\right)^{n-1} \ \ \text{Sum}=\frac{a_1}{1-r}$

Hint (c):

$\text{Sum}=\frac{a}{1-r}$

Answer (d):

The sum would be ∞ because r > 1.