for each of following sequences state whether it converges and if it does to what limit explain your answer to the below An =(6n-3n^3)/(2n^3+4n^2) (n=1,2,3,...)

Question

for each of following sequences state whether it converges and if it does to what limit   explain your answer to the below  An =(6n-3n^3)/(2n^3+4n^2) (n=1,2,3,...)

Damon · Answer

An = 3 n (2- n^2) / [ 2 n^2 (n+2) ] An = (3/2) (1/n) (-1) (n^2-2) /(n+2) as n gets big, 2 looks small An = (-3/2) (1/n) (n^2/n) An = -3/2 (n^2/n^2) An = -3/2