How do you find the common ratio of an infinite geometric series?

Answer 1

Scarlett Allison

You can find the common ratio #r# by finding the ratio between any two consecutive terms.

#r=a_1/a_0=a_2/a_1=a_3/a_2=cdots=a_{n+1}/a_n=cdots#

For the geometric series #sum_{n=0}^infty(-1)^n{2^{2n}}/5^n#, the common ratio

#r=a_1/a_0={-2^2/5}/{1}=-4/5#

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Answer 2

Christopher Allers

To find the common ratio (r) of an infinite geometric series, you divide any term in the series by its preceding term. This can be represented as ( r = \frac{a_{n+1}}{a_n} ), where ( a_{n+1} ) is any term after the first term ( a_1 ), and ( a_n ) is the term preceding ( a_{n+1} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.