IXL - Convergent and divergent geometric series (Precalculus practice)

Does the infinite geometric series converge or diverge?

512

converge

diverge

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Learn with an example

question

Does the infinite geometric series converge or diverge?

converge

diverge

key idea

A sequence is an ordered list of numbers. This list can have a finite number of terms or infinitely many terms.

A series is the sum of a sequence. The infinite series

is geometric if the ratios of consecutive terms are all defined and equal to the same number

(the common ratio of the series).

≥

the series

diverges,

which means it does not equal a number.

the series

converges,

which means it equals a number.

solution

To determine if the series converges or diverges, find the common ratio

If the series converges, find its sum.

Find the common ratio

Take the ratio of the first two terms.

Since the series is geometric, the ratio between any two consecutive terms is 2.

Determine if the series converges or diverges.

Take the absolute value of

≥

Since

≥

the series diverges. Its sum does not exist.

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BB.2Introduction to sigma notation

MM.5Classify formulas and sequences

R.5Division rule for exponents

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