How do you find the sum of the infinite geometric series given #a_1=4# and r=5/7?

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Answer 1 · 2017-02-03T10:36:54

See explanation.

A geometric series is convergent if and only if its ratio #r# is between -1 and 1.

Here the ratio is #r=5/7#, so the series is covergent.

The sum can be calculated as:

#S=a_1/(1-r)#

so here we have:

#S=4/(1-5/7)=4/(2/7)=4*7/2=14#