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Find the sum of the following infinite geometric series, if it exists: 2/5 + 12/25 +72/125 ...

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Tushar Chandra eNotes educator | Certified Educator

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For a geometric series with first term a and common ratio the sum of infinite terms can be determined if `r < 1` and is equal to `a/(1 - r)`

Here, the first term of the series is 2/5 and the common ratio is 6/5

As `6/5 > 1` it is not possible to find the sum of infinite terms.

For the given series the sum of infinite terms cannot be found.

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najm1947 | Student

Common Ratio r = n2/n1 = (12/25)/(2/5) = 6/5 = 1.2

as r is not less than 1 therefore the sum of this series cannot be determined and is infinite.

The sum of infinite terms of a geometric series exists only if r<1 and the sum is equal to a/(1-r) where a is the first term of the series.