# New PDF release: Calculus 3c-2 - Examples of General Elementary Series

By Mejlbro L.

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Extra info for Calculus 3c-2 - Examples of General Elementary Series

Example text

It follows from the laws of magnitudes that an = 5n−1 →∞=0 n2 + n for n → ∞, hence the necessary condition of convergence is not fulﬁlled. 2) Alternatively we get by the criterion of roots that n |an | = n 5 5n−1 = √ → 5 > 1 for n → ∞, √ √ n 2 n n +n 5· n· nn+1 hence the series is divergent. 3) Alternatively every an > 0, so by using the criterion of quotients, 0< n(n + 1) an+1 5n n · → 5 > 1 for n → ∞, = =5· n−1 an (n + 1)(n + 2) 5 n+2 and the series is divergent. 22 Check if the series ∞ n2 + 1 n3 + 1 n=1 is convergent.

In fact, if we choose an = ∞ 1 , then n ∞ an = n=1 1 n n=1 is divergent, and ∞ Please click the advert n=1 a2n ∞ = 1 2 n n=1 is convergent. We have ambitions. Also for you. SimCorp is a global leader in ﬁnancial software. At SimCorp, you will be part of a large network of competent and skilled colleagues who all aspire to reach common goals with dedication and team spirit. We invest in our employees to ensure that you can meet your ambitions on a personal as well as on a professional level. SimCorp employs the best qualiﬁed people within economics, ﬁnance and IT, and the majority of our colleagues have a university or business degree within these ﬁelds.

14 Check if the series ∞ (−1)n √ n−3 n n=10 is convergent or divergent. In case of convergence, check if the series is conditionally convergent or absolutely convergent. √ Necessary condition for convergence? Since n − 3 n > 0 for n ≥ 10, and 1 1 1 √ =√ ·√ →0 n−3 n n n−3 for n → ∞, this condition is fulﬁlled. Absolute convergence? Since 1 1 √ > , n n−3 n ∞ n=10 and 1 is divergent, it follows from the criterion of comparison that the numerical series n ∞ 1 √ n−3 n n=10 is divergent, and the series is not absolutely convergent.

### Calculus 3c-2 - Examples of General Elementary Series by Mejlbro L.

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