Question

这道题怎么写啊🙁🙁🙁

Answer 1

谢谢采纳

Answer 2

n[(1+1/n)^n-e]
=n{e^ln[(1+1/n)^n]-e}
=ne{e^[nln(1+1/n)-1]-1}
原式=lim(n->∞) ne[nln(1+1/n)-1]
=e*lim(n->∞) [nln(1+1/n)-1]/(1/n)
=e*lim(n->∞) [ln(1+1/n)+n/(1+1/n)*(-1/n^2)]/(-1/n^2)
=e*lim(n->∞) [ln(1+1/n)-1/(n+1)]/(-1/n^2)
=e*lim(n->∞) [1/(1+1/n)*(-1/n^2)+1/(n+1)^2]/(2/n^3)
=(e/2)*lim(n->∞) [(n^3)/(n+1)^2-(n^2)/(n+1)]
=(e/2)*lim(n->∞) (-n^2)/(n+1)^2
=-e/2