Power series

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  • #1
quasar987
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If I evaluate the power serie

[tex]y(x) = \sum_{n=0}^{\infty}a_nx^n[/tex]

at x = 0, the first term is [itex]a_0(0)^0[/itex]. But 0^0 is undefined, is it not? How is this paradox solved?
 

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  • #2
Hurkyl
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Because that notation for power series doesn't really mean you're supposed to compute 0^0 to get the n=0 term.

Though, some sources will prefer to write that series as

[tex]y(x) = a_0 + \sum_{n=1}^{\infty}a_nx^n[/tex]

to remove any confusion. (The two mean the same thing, though)
 
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quasar987
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I didn't know that. They don't tell us about any of the subtelties of anything at school. They're totally useless.
 

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