Question

这两个是如何等价的？

如题

Answer 1

ln(1+x) =x-x²/2+x³/3+……+(-1)^(n-1) * x...
x=1/n

Answer 2

n->无穷
ln(1+1/n)= 1/n -(1/2)(1/n^2) +o(1/n^2)
nln(1+1/n)= 1 -(1/2)(1/n) +o(1/n)
nln(1+1/n) -1 =-(1/2)(1/n) +o(1/n)
-e.[nln(1+1/n) -1] =(1/2)(e/n) +o(1/n)
-e.[nln(1+1/n) -1] 等价于 (1/2)(e/n)