I had a mathematical fulguration (is rare because I have troubles with two digits divisions..) and I'd like to know if this is a known fact. In English it goes like:

> The n power of a number a is equal to 1 plus the summation from a**n-1 to a**0 multiplied by n-1

I'm not able to draw it in nice math signs, but in perl is like:

perl -E "map{ $sigma += $ARGV[0]**$_ }0..$ARGV[1]-1; say 'true' if $AR
+GV[0]**$ARGV[1] == 1+( $sigma * ($ARGV[0]-1))"
[download]

In the chat choroba was so kind to prove it mathematically (I leave to him the right to point to that ;)

I proved empirically and works also for powers of 2 (which I already known the formula and in my case becomes a reduced form as it implies * 1 ) and for powers of 1 where it implies * 0

It also works for n**1 and n**0 so it seems a nice generalisation.

Incidentally, there is a nicer way to do the above Σ in perl?

Does some mathematician knows if the above fulguration I had is a known fact?

L*

PS fixed English formula using choroba fix below