2n (1 + n)3n

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Test the series for convergence or divergence.
The image shows the following mathematical expression:

\[
\text{C.} \ \sum_{n=1}^{\infty} \frac{n^{2n}}{(1+n)^{3n}}
\]

This expression represents an infinite series where the terms are determined by the formula \(\frac{n^{2n}}{(1+n)^{3n}}\). The series begins at \(n = 1\) and continues indefinitely. The notation \(\sum\) (sigma) indicates summation, meaning that we add together each term of the series starting from \(n = 1\) to infinity.
Transcribed Image Text:The image shows the following mathematical expression: \[ \text{C.} \ \sum_{n=1}^{\infty} \frac{n^{2n}}{(1+n)^{3n}} \] This expression represents an infinite series where the terms are determined by the formula \(\frac{n^{2n}}{(1+n)^{3n}}\). The series begins at \(n = 1\) and continues indefinitely. The notation \(\sum\) (sigma) indicates summation, meaning that we add together each term of the series starting from \(n = 1\) to infinity.
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