Thursday, February 18, 2010

Fun Math Problem

Evaluate, simplify, and/or approximate the following expression

SUM[ -log( b + (1-b)/(1+b(j-1)) ) ] , FOR j=1,2,...,d

Assume that 0 < b < 1.

This popped up from a discussion I had with Nikos.

Derek said...

Is the answer $\log\frac{2}{b^d+1}$?

Yisong said...

Almost, but not quite =)

Derek said...

Then I think the answer is $\log2 - b^d$? Using the approximation $\log(1+x) \approx x$ when $x$ is small enough?

Yisong said...