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Section 10.1 : Sequences

For problems 1 & 2 list the first 5 terms of the sequence.

1. \(\left\{ {\displaystyle \frac{{4n}}{{{n^2} - 7}}} \right\}_{n = 0}^\infty \) Solution
2. \(\left\{ {\displaystyle \frac{{{{\left( { - 1} \right)}^{n + 1}}}}{{2n + {{\left( { - 3} \right)}^n}}}} \right\}_{n = 2}^\infty \) Solution

For problems 3 – 6 determine if the given sequence converges or diverges. If it converges what is its limit?

1. \(\left\{ {\displaystyle \frac{{{n^2} - 7n + 3}}{{1 + 10n - 4{n^2}}}} \right\}_{n = 3}^\infty \) Solution
2. \(\left\{ {\displaystyle \frac{{{{\left( { - 1} \right)}^{n - 2}}{n^2}}}{{4 + {n^3}}}} \right\}_{n = 0}^\infty \) Solution
3. \(\left\{ {\displaystyle \frac{{{{\bf{e}}^{5n}}}}{{3 - {{\bf{e}}^{2n}}}}} \right\}_{n = 1}^\infty \) Solution
4. \(\left\{ {\displaystyle \frac{{\ln \left( {n + 2} \right)}}{{\ln \left( {1 + 4n} \right)}}} \right\}_{n = 1}^\infty \) Solution