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an = 2n dn= (n)² २

an = 2n dn= (n)² २

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Exercise: Determine Divergence of Sequences** 1. For each of the following sequences, show that it is divergent: a) \( a_n = 2n \) b) \( d_n = (1 - n)^2 \) ### Explanation: For sequence (a), \( a_n = 2n \) – it is a linear sequence that increases indefinitely as \( n \) increases. For sequence (b), \( d_n = (1 - n)^2 \) – it represents a quadratic sequence that grows indefinitely as \( n \) increases, since subtracting a larger number and squaring results in an increasingly large positive number. Both sequences do not converge to a finite limit.
Transcribed Image Text:**Exercise: Determine Divergence of Sequences** 1. For each of the following sequences, show that it is divergent: a) \( a_n = 2n \) b) \( d_n = (1 - n)^2 \) ### Explanation: For sequence (a), \( a_n = 2n \) – it is a linear sequence that increases indefinitely as \( n \) increases. For sequence (b), \( d_n = (1 - n)^2 \) – it represents a quadratic sequence that grows indefinitely as \( n \) increases, since subtracting a larger number and squaring results in an increasingly large positive number. Both sequences do not converge to a finite limit.
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