They claim that the trivial 0s (zeta(z)=0) occur when z is a negative odd integer (with no imaginary component). But it seems obviously wrong. Take z=-2 zeta(-2)=1+1/(2^-2)+1/(3^-2).... =1+4+9.... Obviously this series will not equal 0. Where have I gone wrong? Have I misunderstood the meaning of 'zeros of the zeta function'?