If the following infinite geometric series converges, find its sum.
1 + 1.2 + 1.2² + 1.2³ ...
Answers Choices:
A) 120
B) 144
C)120,000
D) 1.2 x 10¹²
E) The series does not converge.
Can you please show me how to do this problem?? Thank you!
llaffer
Favorite Answer
The first term is 1 and the common ratio is 1.2.
Since the ratio is more than 1, this won't converge.
It will only converge if the common ratio is: -1 < r < 1 and r ≠ 0.
If it did converge, you could use this equation to find the sum:
S = a / (1 - r)
Where a is the first term and r is the common ratio.
stanschim
Since the absolute value of the multiplying factor, 1.2, is greater than or equal to 1, this series does not converge. In order for a geometric series to converge, the absolute value of the multiplying factor must be less than 1.
E.