10.1-bo'lim : Ketma-ketliklar

1-3-muammolar uchun ketma-ketlikning dastlabki 5 ta shartini ko'rsating.

1. \(\left\{ {{{\left( { - 1} \right)}^n}{{\bf{e}}^{2n}}} \right\}_{n = 1}^\infty \)
2. \(\left\{ {\displaystyle \frac{{6 - 8n}}{{{n^2} + 9n}}} \right\}_{n = 2}^\infty \)
3. \(\left\{ {\displaystyle \frac{4}{{{{\left( { - 2} \right)}^{n + 1}} + {3^n}}}} \right\}_{n = 1}^\infty \)

4-10-masalalar uchun berilgan ketma-ketlikning yaqinlashish yoki uzoqlashishini aniqlang. Agar u yaqinlashsa, uning chegarasi qancha?

1. \(\left\{ {\displaystyle \frac{{5 + {n^3}}}{{2{n^2} - 8n + 1}}} \right\}_{n = 0}^\infty \)
2. \(\left\{ {\displaystyle \frac{{6{n^4} + 9{n^2}}}{{9{n^4} - 8{n^2} + 7}}} \right\}_{n = 11}^\infty \)
3. \(\left\{ {\displaystyle \frac{{{{\left( { - 1} \right)}^{n + 7}}\left( {2 - 8n} \right)}}{{{n^2} + 9}}} \right\}_{n = 2}^\infty \)
4. \(\left\{ {\cos \left( {n\pi } \right)} \right\}_{n = 0}^\infty \)
5. \(\left\{ {\displaystyle \frac{{n + 1}}{{\ln \left( {6n} \right)}}} \right\}_{n = 2}^\infty \)
6. \(\left\{ {\cos \left( {\displaystyle \frac{3}{{n + 1}}} \right)} \right\}_{n = 1}^\infty \)
7. \(\left\{ {\ln \left( {4n + 1} \right) - \ln \left( {2 + 7n} \right)} \right\}_{n = 0}^\infty \)