Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Sequence and Series
A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.
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*You cannot use any theorems about convergent sequences*

Using the definition of a convergent sequence, prove:

 

The expression shown in the image is a mathematical limit: \[ \lim_{{n \to \infty}} \frac{n}{2n-1} = \frac{1}{2} \] This limit describes the behavior of the fraction \(\frac{n}{2n-1}\) as \(n\) approaches infinity. As \(n\) becomes very large, the value of the fraction approaches \(\frac{1}{2}\). This is because the highest degree terms in the numerator and the denominator dominate, simplifying the expression to \(\frac{1}{2}\) in the limit.
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Transcribed Image Text:The expression shown in the image is a mathematical limit: \[ \lim_{{n \to \infty}} \frac{n}{2n-1} = \frac{1}{2} \] This limit describes the behavior of the fraction \(\frac{n}{2n-1}\) as \(n\) approaches infinity. As \(n\) becomes very large, the value of the fraction approaches \(\frac{1}{2}\). This is because the highest degree terms in the numerator and the denominator dominate, simplifying the expression to \(\frac{1}{2}\) in the limit.
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