Chapter 8: Q30RE (page 498)
Express the repeating decimal \({\rm{4}}{\rm{.17326326326 \ldots \ldots }}\)as a fraction.
The fraction with a repeating decimal is\(\frac{{{\rm{416909}}}}{{{\rm{99900}}}}\).
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.
\({a_n} = \frac{{{{(\ln n)}^2}}}{n}\)
Determine whether the series is convergent or divergent:\(\sum\limits_{n = 0}^\infty {\frac{{1 + \sin n}}{{{{10}^n}}}} \).
Find the limits of the sequences\(\left( {\sqrt 2 ,\sqrt {2\sqrt 2 } ,\sqrt {2\sqrt {2\sqrt 2 } } ,........} \right)\).
What can you say about the series \(\sum {{a_n}} \) in each of the following cases?
(a) \(\mathop {lim}\limits_{n \to \infty } \left| {\frac{{{a_{n + 1}}}}{{{a_n}}}} \right| = 8\)
(b) \(\mathop {lim}\limits_{n \to \infty } \left| {\frac{{{a_{n + 1}}}}{{{a_n}}}} \right| = 0.8\)
(c) \(\mathop {lim}\limits_{n \to \infty } \left| {\frac{{{a_{n + 1}}}}{{{a_n}}}} \right| = 1\)
Determine whether the sequence converges or diverges. If it converges, find the limit.
\({a_n} = \sqrt {\frac{{n + 1}}{{9n + 1}}} \)
What do you think about this solution?
We value your feedback to improve our textbook solutions.
