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5.045 Limiting sums

Interactive practice questions

What condition must be satisfied by an infinite geometric series in order for its sum to exist?

the absolute value of the common ratio must be less than $1$1

A

the common ratio must be negative

B

the common ratio must be less than $1$1

C

the common ratio must be greater than $1$1

D

the absolute value of the common ratio must be greater than $1$1

E
Easy
< 1min

Consider the infinite geometric sequence: $2$2, $\frac{1}{2}$12, $\frac{1}{8}$18, $\frac{1}{32}$132, $\ldots$

Easy
1min

Consider the infinite geometric sequence: $125$125, $25$25, $5$5, $1$1, $\ldots$

Easy
1min

Consider the infinite geometric sequence: $16$16, $-8$8, $4$4, $-2$2, $\ldots$

Easy
1min
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Outcomes

MA12-2

models and solves problems and makes informed decisions about financial situations using mathematical reasoning and techniques

MA12-4

applies the concepts and techniques of arithmetic and geometric sequences and series in the solution of problems

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