Use the formula for the sum of a geometric series to find the sum or state that the series diverges (enter DIV for a divergent series). sum_{n=2}^inftyfrac{5^n}{12^n}

texelaare 2020-12-21 Answered
Use the formula for the sum of a geometric series to find the sum or state that the series diverges (enter DIV for a divergent series).
n=25n12n
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Expert Answer

broliY
Answered 2020-12-22 Author has 97 answers
Here, the given series is
n=25n12n
Let us expand the given series.
n=25n12n=52122+53123+54124+... (up to )
=(512)2+(512)3+(512)4+...
We clearly see that the given series is an infinite geometric series with first term (512)2 and common ratio (512).
Again, We know that the sum of an infinite geometric series with first term a(say) and common ratio r(|r|1) is a1r
So, n=25n12n=521221512
=25144712
=25144×127
=2584
Which is the required answer.
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Jeffrey Jordon
Answered 2021-12-16 Author has 2313 answers

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