The limit is $$\lim_{x \to \infty} \left[ {x^{x+1} \over (x+1)^x} - { (x-1)^x\over x^{x-1}}\right]$$
Experimentally, this limit appears to converge to ${1 \over e}$, but I can't figure out how to solve it.
The limit is $$\lim_{x \to \infty} \left[ {x^{x+1} \over (x+1)^x} - { (x-1)^x\over x^{x-1}}\right]$$
Experimentally, this limit appears to converge to ${1 \over e}$, but I can't figure out how to solve it.