- #1
nuclearrape66
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does the series from 1 to infinity of [tex]\sum[/tex](1 - (2/n))^3n convegre or diverge.
i've tried almost all the tests and can't figure it out...
i've tried almost all the tests and can't figure it out...
nuclearrape66 said:are you saying do the terms get closer to zero? yes.
The formula for the series is $\sum (1 - \frac{2}{n})^3n = \frac{n}{n^3-6n^2+12n-8}$.
The series converges.
The limit of the series is 1.
The convergence test for the series is the ratio test.
The number of terms needed will depend on the error margin and can be calculated using the error bound theorem.