INFINITE GEOMETRIC SERIES
Flashcard
•
Mathematics
•
10th - 12th Grade
•
Practice Problem
•
Hard
Standards-aligned
Wayground Content
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15 questions
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1.
FLASHCARD QUESTION
Front
What is an infinite geometric series?
Back
An infinite geometric series is the sum of the terms of a geometric sequence that continues indefinitely. It converges if the absolute value of the common ratio is less than 1.
2.
FLASHCARD QUESTION
Front
What is the formula for the sum of an infinite geometric series?
Back
The sum S of an infinite geometric series with first term a and common ratio r (|r| < 1) is given by: S = a / (1 - r).
3.
FLASHCARD QUESTION
Front
Given the first term 318 and common ratio 1/2, what is the sum of the infinite geometric series?
Back
The sum is 636.
4.
FLASHCARD QUESTION
Front
Evaluate the infinite geometric series: 3 - 2 + 4/3 - 8/9 + ...
Back
The sum is 9/5.
5.
FLASHCARD QUESTION
Front
Back
The sum is 5.
6.
FLASHCARD QUESTION
Front
What does it mean if a geometric series diverges?
Back
A geometric series diverges if the absolute value of the common ratio is greater than or equal to 1, meaning the sum does not approach a finite limit.
7.
FLASHCARD QUESTION
Front
Find the sum of the infinite geometric series: 200 - 100 + 50 - 25 + ...
Back
The sum is 400/3.
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