[(2n+3n)/( 2n+1+3n+1)]的极限,n趋于无穷

题目

[(2n+3n)/( 2n+1+3n+1)]的极限,n趋于无穷

答案

上下除以3^n
原式=lim[(2/3)^n+1]/[2*(2/3)^n+3]
(2/3)^n趋于0
所以原式=(0+1)/(0+3)=1/3