I'm a CS major, and I'm learning about trees and time complexity. I want to know if it always holds that b (the branching factor of a tree) to the power of d (the depth of the tree) is the sum of all prior levels plus 1.
More formally: b^d = 1 + b^0 + b^1 . . . b^d-1
And whence comes the "1+" at the beginning? Isn't that what b^0 is for*? I can see a sort of pattern here, but the 1 throws me off. Would calculus help me be a better programmer? I loved my discrete mathematics curriculum -- is analysis related as well?
*i.e., is this why raising to the zeroth power = 1?