The annual demand for box lunch in fast food restaurants is a function of x and price p.

Prove a > = 1 by mathematical induction.

If n! (e/n)^n>； = 1, then

(n+ 1)！ (e/(n+ 1))^(n+ 1)

=n！ (e/n)^n*e/( 1+ 1/n)^n

& gt=e/( 1+ 1/n)^n.

Because (1+ 1/n) n is strictly increasing towards E, it is necessary.

( 1+ 1/n)^n= 1.

So we know that the series diverges.

In fact, it is easy to know Stirling formula.