Answered

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Does this sequence converge or diverge? \left\{\frac{10n-6}{2n-3}\right\} { 2n−3 10n−6 ​ }

Sagot :

abidemiokin

Answer:

The sequence converges

Step-by-step explanation:

Given the sequence Un = 10n-6/2n-3

To determine whether the sequence converges or diverges, we will have to take the limit of the sequence as n goes large.

[tex]\lim_{n \to \infty} \left\{\frac{10n-6}{2n-3}\right}\\[/tex]

Divide through by n

[tex]= \lim_{n \to \infty} \left\{\frac{10n/n-6/n}{2n/n-3/n}\right}\\= \lim_{n \to \infty} \left\{\frac{10-6/n}{2-3/n}\right}\\= \left\{\frac{10-6/\infty}{2-3/\infty}\right}\\= \frac{10-0}{2-0}\\= 10/2\\= 5[/tex]

Since the limit of the sequence gives a finite value, hence the sequence converges

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