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Mathematik-Online problems:

Problem 125: Criterion for Limits

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

a)
Let $ (a_n)$ and $ (b_n)$ be two real sequences with positive elements. Proof: If the sequence of the quotients $ a_n/b_n$ has a positive limit, the series $ \sum a_n$ and $ \sum b_n$ have the same behaviour with respect to convergence.
b)
Is the series $ {\displaystyle{\sum_{n=0}^\infty \frac{n^5+3n+2}{n^6+17}}}$ convergent?

(Authors: Apprich/Höfert)

see also:

[Solutions]
  automatisch erstellt am 14. 10. 2004