Chapter 8: Q31E (page 443)
Express the number as a ratio of integers \(0.\bar 8 = 0.888888....\)
The ratio of \(0.\bar 8 = \frac{8}{9}\)
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\(\frac{1}{3} + \frac{1}{6} + \frac{1}{9} + \frac{1}{{12}} + \frac{1}{{15}} + ......\)
Find the limits of the sequences\(\left( {\sqrt 2 ,\sqrt {2\sqrt 2 } ,\sqrt {2\sqrt {2\sqrt 2 } } ,........} \right)\).
If\({\bf{\$ 1000}}\)is invested at\({\bf{6\% }}\) interest, compounded annually, then after\({\bf{n}}\)years the investment is worth \({{\bf{a}}_{\bf{n}}}{\bf{ = 1000(1}}{\bf{.06}}{{\bf{)}}^{\bf{n}}}\)dollars.
(a) Find the first five terms of the sequence\(\left\{ {{{\bf{a}}_{\bf{n}}}} \right\}\).
(b) Is the sequence convergent or divergent? Explain.
Determine whether the series is convergent or divergent. If its convergent, find its sum.
\(\sum\limits_{n = 1}^\infty {\frac{{(n - 1)}}{{(3n - 1)}}} \)
Find the values of x for which the series converges. Find the sum of the series for those values of x.
\(\sum\nolimits_{n = 0}^\infty {\frac{{{{(x - 2)}^n}}}{{{3^n}}}} \)
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