Recent content by jsmith

My mistake, I missread 1 as 0. But it doesn't change much. If the sum of f(k) from k=1 to n (btw, don't use n as both the thing you are summing over as well as the number of terms you are summing) for all n, then you must have f(1)=1 and all others are 0. To see this just set n=1 so f(1)=1 then...

Thanks for the replies. I do understand fully why this identity holds. I guess my question is why should a completely geometric concept (pi) be linked so nicely with a completely analytical constant (e). Thinking about it I am wondering if this is anything to do with the fact that e is defined...

Can you clarify, is the formula meant to hold for all n or for a fixed value of n? If it is for all n the f(n)=0 is the only solution in this case. If it is for a fixed n then there are infinite f(n) that will work.

I will first say that I fully understand how to prove this equation from the use of power series, what I am interested in though is why e and pi should be linked like they are. As far as I know pi comes from geometry (although it does have an equivalent analytical definition), and e comes from...