The solution of LIM [(3N & # 178; + N + 5) / (n & # 179; + 3N + 1)]
The numerator and denominator are divided by n ^ 3 at the same time
lim(3/n+1/n^2+5/n^3)/(1+3/n^2+1/n^3)=0
The solution of LIM (n →∞) [(3N & # 178; + N + 5) / (n & # 179; + 3N + 1)]
Prove LIM (2 ^ n / N!) by definition
It is proved that for any given ε > 0, if the
│2^n/n!-0│=2^n/n!<ε
2^n/n!=(2/1)(2/2)...(2/n)=2(2/3)(2/4)...(2/n)< 2/n