大佬来看看,孩子做不出来啊。

y->0+
1/(1-y)= 1+y +o(y)
1/(1-2y)= 1+2y +o(y)
...
1/(1-ny) =1+ny +o(y)
1/[(1-y)(1-2y)...(1-ny)]
=[1+y +o(y)].[1+2y +o(y)]...[1+ny +o(y)]
=1+[n(n+1)/2]y +o(y)
lim(x->+∞) { x^n/[(x-1)(x-2)...(x-n)]}^(2x)
y=1/x
=lim(y->0+) { (1/y)^n/[(1/y-1)(1/y-2)...(1/y-n)]}^(2/y)
=lim(y->0+) { 1/[(1-y)(1-2y)...(1-ny)]}^(2/y)
=lim(y->0+) { 1+[n(n+1)/2]y }^(2/y)
= e^[n(n+1)]

加个一减个一