Evaluating Infinite Geometric Series

Flashcard
•
Mathematics
•
9th - 12th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a geometric series?
Back
A geometric series is the sum of the terms of a geometric sequence, where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
2.
FLASHCARD QUESTION
Front
How do you find the sum of the first n terms of a geometric series?
Back
The sum of the first n terms (S_n) of a geometric series can be calculated using the formula: S_n = a(1 - r^n) / (1 - r), where a is the first term and r is the common ratio.
3.
FLASHCARD QUESTION
Front
What is the formula for the sum of an infinite geometric series?
Back
The sum of an infinite geometric series exists if the absolute value of the common ratio r is less than 1. The formula is S = a / (1 - r), where a is the first term.
4.
FLASHCARD QUESTION
Front
What condition must be met for an infinite geometric series to converge?
Back
For an infinite geometric series to converge, the absolute value of the common ratio (|r|) must be less than 1.
5.
FLASHCARD QUESTION
Front
Back
Does Not Exist (the series diverges because the common ratio is greater than 1).
6.
FLASHCARD QUESTION
Front
Back
7.
FLASHCARD QUESTION
Front
What is the common ratio in a geometric series?
Back
The common ratio (r) is the factor by which each term is multiplied to get the next term in the series.
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