Ramanujan Summation not consistent with Riemann's Zeta function?

Ramanujan Summation not consistent with Riemann's Zeta function?

Wikipedia states that Ramanujan sums and the Riemann Zeta function have
the same values for even $k$:
$$1 + 2^{2k} + 3^{2k} + \cdots = 0\ (\Re)$$
However, I don't understand how this can be true, because when $k = 0$,
because that gives us:
$$1 + 1 + 1 + \cdots = \sum_{n=1}^\infty n^{0} = 0\ (\Re)$$
and yet we have $\zeta(0) = -1/2$, which are clearly unequal.
What am I doing wrong?