I was wondering if anyone has a trick to do the following problem:
1. 1+2+2^2 + ... + 2^9 = _____________
answer (1023)
so basically i am looking for a formula in two variables, the base, b, and the highest power, n; generally, that would be
b^0 + b^1 + b^2 + b^3 ... + b^n
from the first example it would seem that the formula is b^(n+1) - 1, but that doesn't work for everything I tried.
Anyone have any ideas?
Vinay
I think I've found it.
It looks like the formula is :
(b^(n+1) - 1)/(b-1)
So far, it's worked for everything I tried
sorry....mis post....
(a-1)a^0 + (a-1)a^1 + (a-1)a^2 + .... + (a-1)a^n = a^(n+1)-1
we factor out (a-1) from the left and derive the formula (a^(n+1)-1)/(a-1)
just giving everyone an idea of how it was derived
