Re: The Reimann "Zeta" function: How can it ever converge?

So I was reading in Wikipedia about the Zeta function, which is defined as:
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    Z(s) = 1/(1**s) + 1/(2**s) + 1/(3**s) + ...
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Both the domain and range are specified as the complex numbers.
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And it says that if s is a negative integers (-2, -4, -6, etc), then Z(s)
is zero.  But that can't be right.  But first, a little manipulation:
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Suppose s is -2:
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    1/(n**s), where s = -2
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is:
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    1/(1/(n**2))
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is:
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    n**2
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so, the sum is like:
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    1+4+9+16+25+...
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Which just grows without bounds.  And is certainly never zero.
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So, is Wikipedia wrong?  Or just a typo?