geometrische functies

sum(z^k, k=n..m-1) = (z^n - z^m ) / (1-z)

sum((k+1)*z^k, k=n..m-1) = (n*z^n-m*z^m)/(1-z) + (z^n-z^m)/(1-z)^2

sum(k^-m, k>=1) = (2*pi)^m * abs(bern(m)) / (2 * fac(m) ), voor m even

sum(k^m, k=0..n) = (n+1)/(m+1) * sum( binom(m+1, k) * bern(k) * (n+1)^(m-k) , k=0..m)

bern(k) = bernoulli getallen:

coefficients of taylor expansion of t/(exp(t)-1) = sum(t^k/fac(k) * bern(k), k>=0)

or sum( sum( (-1)^r * r^n * binom(k, r) , r=0..k ) / (k+1), k=0..n)

1, -1/2, 1/6, -1/30, 1/42, -1/30, 5/66, ....

fac(k) = k!

binom(n,k) = n!/( k! * (n-k)! )