Chapter 8: Q20E (page 463)
Determine whether the series is absolutely convergent, conditionally convergent,or divergent.
\(\sum\limits_{n = 1}^\infty {\frac{{{{( - 2)}^n}}}{{{n^2}}}} \)
The Series is Divergent.
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
Determine whether the sequence converges or diverges. If it converges, find the limit.
\({a_n} = \cos \left( {\frac{2}{n}} \right)\)
Determine whether the series is convergent or divergent:\(\sum\limits_{n = 0}^\infty {\frac{{1 + \sin n}}{{{{10}^n}}}} \).
Use definition 2 directly to prove that \(\mathop {\lim }\limits_{n \to \infty } {(0.8)^n} = 0\)(from ? with, \(r = 0.8\)). Use logarithms to determine how large n has to be so that \((0.8) < 0.000001\).
Calculate the first eight terms of the sequence of partial sums correct to four decimal places. Does it appear that the series is convergent or divergent?
\(\sum\limits_1^\infty {\frac{{{{( - 1)}^{n - 1}}}}{{n!}}} \)
Find the first 40 terms of the sequence defined by\({a_{n + 1}} = \left\{ {\begin{aligned}{\frac{1}{2}{a_n}}&{{\rm{ if }}{a_n}{\rm{ is an even number }}}\\{3{a_n} + 1}&{{\rm{ if }}{a_n}{\rm{ is an odd number }}}\end{aligned}} \right.;{a_1} = 11\).
Do the same if\({a_1} = 25\). Make a conjecture about this type of sequence
What do you think about this solution?
We value your feedback to improve our textbook solutions.
