Question

关于高数极限证明的几道题 证明 1.lim(xn)=n^2/(2n^3+1)=0 2.lim(3n+1)/(2n-1)=

Answer 1

1、limn^2/(2n^3 +1) =lim(1/n) / (2 + 1/n^3)

∵n→∞时,1/n→0,1/n^3 →0

所以原式=0

2、lim(3n+1)/(2n-1) = lim(3+ 1/n) / (2- 1/n) = 3/2

3、2^n/n!= 2^n/(1*2*3*...*n) < 2^n/(1*2*3*3*3...*3) = 2*(2/3)^(n-2)

所以0