Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
For each sequence below, determine the limit as \( n \to \infty \). If a limit is infinite, write "\(\infty\)" or "\(-\infty\)". a) Let \( a_n = \frac{5n^{100} - 2n^n}{n! + \ln(n)} \). Then \( \lim_{n \to \infty} a_n = \) \(\underline{\hspace{3cm}}\) b) Let \( a_n = \frac{2^{3n+3} + 6^n}{7 \cdot 8^n + 15n^2} \). Then \( \lim_{n \to \infty} a_n = \) \(\underline{\hspace{3cm}}\)
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Transcribed Image Text:For each sequence below, determine the limit as \( n \to \infty \). If a limit is infinite, write "\(\infty\)" or "\(-\infty\)". a) Let \( a_n = \frac{5n^{100} - 2n^n}{n! + \ln(n)} \). Then \( \lim_{n \to \infty} a_n = \) \(\underline{\hspace{3cm}}\) b) Let \( a_n = \frac{2^{3n+3} + 6^n}{7 \cdot 8^n + 15n^2} \). Then \( \lim_{n \to \infty} a_n = \) \(\underline{\hspace{3cm}}\)
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