Question

[(n+2)/(n+1)*n/(n+1)]的(n+1）次方求极限,n趋近无限大

Answer 1

lim(n→∞)[(n+2)n/(n+1)^2]^(n+1)

=lim(n→∞)[(n^2+2n)/(n^2+2n+1)]^(n+1)

=lim(n→∞)[1-1/(n+1)^2]^(n+1)

=lim(n→∞)[1+1/(n+1)]^(n+1) *[ [1-1/(n+1)]^(-(n+1))]^(-1)

=e*1/e=1