#### noelevans wrote:

How does this look? :0)

i*180 i*(180/n) i0

(-1)^(1/n) = (1*e )^(1/n) = 1*e so this approaches 1*e = 1 as n goes to infinity.

(The angles are in degrees.)

I have to admit that at first sight this looked funny; but after being (maybe) less superficial i'm seeing a meaning behind this:

look it geometrically (i write polar coordinates for complex numbers)...

the (first) square root for -1 is (1,pi/2) (midnight)

the (first) 3rd root for -1 (1,pi/3) (one o'clock)

the (first) 4th root for -1 is (1,pi/4) (half past one)

.....

..... (...some time passes...)

.....

the (first) nth root for -1 tends to (1,0) (almost three o' clock)

so it seems to me that your limit is what the first nth root of (-1) tends to.

EDIT: I want to add something:

where k=0,1,2...,n-1. In particular, the integer part of (n+1)/2 (which is n/2 if n is even and (n+1)/2 if odd) belongs to the list of k's;

If we accept your and my proceeding then we get:

(where i put n/2 or n+1/2 as k)

so one of us (or eventually both

) must be wrong.