Solve for all x such that:

Question

(1+(1/x))^(x+1)=(2000/1999)^1999

Answer 1

I find only one root at about
x=2.7176022...
a reasonable approximation to e.

Answer 2

Hmmm. That's not what I get.

(1+(1/2.7176022)) = 1.36797
1.36797^3.7176022 = 2.20537

(2000/1999)^1999 = 2.7176022

close, but not nearly correct.

(1+1/e)^(e+1) = 3.20527

I get a solution at x = -2000

(1+(1/-2000))^(-2000+1) = 2.7176022

Answer 3

Very true, x=-2000 solves the problem exactly.
Please disregard solution x=2.7176022...