Chapter 8: Q10E (page 443)
Determine whether the geometric series is convergent or divergent..If it is convergent,find its sum.
\(\sum\limits_{n = 1}^\infty {\frac{{{{(10)}^n}}}{{{{( - 9)}^{n - 1}}}}} \)
The given series is Divergent..\(\)
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Show that the sequence defined by \({a_1} = 2,{a_{n + 1}} = \frac{1}{{3 - {a_n}}}\) sequences \(0 < {a_n} \le 2\) and is decreasing . Deduce that the sequence is covering and find its limit.
Determine whether the sequence converges or diverges. If it converges, find the limit.
\({a_n} = \ln \left( {2{n^2} + 1} \right) - \ln \left( {{n^2} + 1} \right)\)
Determine whether the series is convergent or divergent. If its convergent, find its sum.
\(\sum\limits_{n = 1}^\infty {\frac{{(n - 1)}}{{(3n - 1)}}} \)
\({\bf{37 - 40}}\) Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?
\({a_n} = \frac{{2n - 3}}{{3n + 4}}\)
Show that the series is convergent. How many terms of the series do we need to add in order to find the sum to the indicated accuracy?
\(\sum\limits_{n = 0}^\infty {\frac{{{{( - 1)}^n}}}{{{{10}^n}n}}} \) (error \(| < 0.000005\))
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