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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].

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