Chapter 8: Q18RE (page 498)
Determine whether the series is convergent or divergent.
\(\sum\limits_{{\rm{n = 1}}}^\infty {\frac{{{{\left( {{\rm{ - 5}}} \right)}^{{\rm{2n}}}}}}{{{{\rm{n}}^{\rm{2}}}{{\rm{9}}^{\rm{n}}}}}} \)
The Root Test shows that the provided series is divergent.
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\({\bf{37 - 40}}\) Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?
\({a_n} = \frac{1}{{2n + 3}}\)
(a) If \(\left\{ {{{\bf{a}}_{\bf{n}}}} \right\}\)is convergent, show that\(\mathop {\lim }\limits_{n \to \infty } {a_{n + 1}} = \mathop {\lim }\limits_{n \to \infty } {a_n}\).
(b) A sequence\(\left\{ {{{\bf{a}}_{\bf{n}}}} \right\}\)is defined by \({a_1} = 1\)and \({a_{n + 1}} = 1/\left( {1 + {a_n}} \right)\)for. Assuming that \(\left\{ {{a_n}} \right\}\)is convergent, find its limit.
Determine whether the sequence converges or diverges. If it converges, find the limit.
\({a_n} = {2^{ - n}}\cos n\pi \)
\(\sum\limits_{n = 1}^\infty {\arctan (n)} \) Find Whether It Is Convergent Or Divergent And Find Its Sum If It Is Convergent.
Express the number as a ratio of integers.
\(\)\(0.\overline {46} = 0.46464646...\)
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