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Section 10.4 : Convergence/Divergence of Series
For problems 1 & 2 compute the first 3 terms in the sequence of partial sums for the given series.
- \( \displaystyle \sum\limits_{n = 1}^\infty {n\,{2^n}} \) Solution
- \( \displaystyle \sum\limits_{n = 3}^\infty {\frac{{2n}}{{n + 2}}} \) Solution
For problems 3 & 4 assume that the \(n\)th term in the sequence of partial sums for the series \( \displaystyle \sum\limits_{n = 0}^\infty {{a_n}} \) is given below. Determine if the series \( \displaystyle \sum\limits_{n = 0}^\infty {{a_n}} \) is convergent or divergent. If the series is convergent determine the value of the series.
- \(\displaystyle {s_n} = \frac{{5 + 8{n^2}}}{{2 - 7{n^2}}}\) Solution
- \(\displaystyle {s_n} = \frac{{{n^2}}}{{5 + 2n}}\) Solution
For problems 5 & 6 show that the series is divergent.