Answered

Discover new perspectives and gain insights with IDNLearn.com's diverse answers. Our platform offers detailed and accurate responses from experts, helping you navigate any topic with confidence.

Determine if the sequence An is convergent. If the sequence is convergent, state its limit. If the series diverges, mark the sequence as either Divergent or Divergent because the sequence is unbounded (or -) S13 18 23 28 33 8 5n An 5 8 11 14 17 2 3n Convergent sequence whose limit is O Divergent O Divergent because the sequence is unbounded (or - 00)

Sagot :

Answer:

The answer is "[tex]\frac{5}{3}[/tex]"

Step-by-step explanation:

[tex]A_n={\frac{13}{5},\frac{18}{8},\frac{23}{11},\frac{28}{14},\frac{33}{17},..................\frac{8+5n}{2+3n}}\\\\[/tex]

[tex]\to A_n=\frac{8+5n}{2+3n}\\\\\to \lim_{n \to \infty} A_n = \lim_{n \to \infty} \ \frac{8+5n}{2+3n}= \lim_{n \to \infty} \ \frac{\frac{8}{n}+5}{\frac{2}{n}+3}=\frac{0+5}{0+3}=\frac{5}{3}[/tex]

In this sequence An is convergents where limits are [tex]\frac{5}{3}[/tex].

Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Thank you for choosing IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more solutions.