Question

Find the sum of an infinite geometric sequence in which a1=100
and r=67.

Sum =

Answer 1

To find the sum of an infinite geometric series, we can use the formula:

\[
S = \frac{a_1}{1 - r}
\]

where \( S \) is the sum of the series, \( a_1 \) is the first term, and \( r \) is the common ratio.

In your case, you have:

- \( a_1 = 100 \)
- \( r = 67 \)

However, for the formula to be valid, the absolute value of the common ratio \( |r| \) must be less than 1:

\[
|r| < 1
\]

Since \( r = 67 \), which is greater than 1, the series diverges. Therefore, the sum of this infinite geometric series does not exist.

In summary:

\[
\text{The sum } S = \text{undefined (the series diverges)}
\]