Given:An = [6 n/(-4 n + 9)]For both of the following answer blanks, decide whether the given sequence or series is convergent or divergent. If convergent, enter the limit (for a sequence) or the sum (for a series). If divergent, enter INF if it diverges to infinity, MINF if it diverges to minus infinity, or DIV otherwise.(a) The sequence {An }._________________(b) The series βˆ‘n=1[infinity]( An )________________

Accepted Solution

Answer:The sequence is convergent and the serie is divergent.Step-by-step explanation:Sequence:We calculate the limit when n tends to infinity to see if it is convergent or divergent:[tex]\lim_{n \to \infty} \frac{6n}{-4n+9} = \frac{6}{-4} = \frac{-3}{2} \neq 0[/tex] then, the sequence is convergent.Serie:[tex]\sum_{n=1}^{\infty} (\frac{6n}{-4n+9})[/tex]. To know if it converges we are going to use the limit test:[tex]\lim_{n \to \infty} a_n[/tex]. If this limit is non equal to 0 the serie diverges. [tex]\lim_{n \to \infty} \frac{6n}{-4n+9} = \frac{6}{-4} = \frac{-3}{2} \neq 0[/tex], then the serie diverges.