21 Jul
2010
21 Jul
'10
5:52 p.m.
Rich wrote: << H(2n) - H(n) -> log2 = .693... for large N. The H difference can be thought of as the area of a staircase, with steps of width 1/n and height n/k from the x-axis, as k goes from n+1 to 2n. [The height is from a fixed baseline; the drop from one step to the next is much smaller.] The staircase is a good approximation to the curve 1/x, 1<x<2, whose integral is log2.
Yes. Also, unvarnished H(2n) - H(n) is a very good approximation to log(2n) - log(n) = log(2). --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele