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Mathematik-Online problems:

Problem 91: Convergence ans Limits of Sequences


A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Analyse if the given sequences are convergent and give the limit for each convergent sequence.

a) $ a_n={\displaystyle{\frac{(3n-4)(n^2+1)}{7n\,(2n^2+10000)}}}$  b) $ a_n={\displaystyle{n\left(1-\sqrt{1-\frac{c}{n}}\; \right),}}
\quad c\leq 1$
c) $ a_n={\displaystyle{\left(1-\frac{c}{n}-\frac{c^2}{n^3}\;\right)^{\!n},}}
\quad c\in\mathbb{R}$  d) $ a_n={\displaystyle{{\mathrm{sp}}(A^n), \quad
A=\left(\begin{array}{cc} 0 & {\mathrm{i}} \\ {\mathrm{i}} & 0\end{array}\right)}}$
e) $ a_n={\rm {e}}^{-\frac{1}{3}n\pi}$  f) $ a_n={\rm {e}}^{-\frac{1}{3}n\pi{\mathrm{i}}}$

(Authors: Kirchgässner/Werner/Hesse/Apprich/Höfert)

see also:


[Solutions]

  automatisch erstellt am 13. 12. 2007