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Problem:

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Define

[tex] f_{n}(x)=n^{\alpha}, |x|\leq 1/n, f_{n}=0[/tex] elsewhere

Give all [tex]\alpha \in \Re [/tex] for which

[tex] \lim_{n \to \infty} \int_{\Re}f_{n}(x)dx=+\infty [/tex]

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Can i change this last integral to:

[tex] \lim_{x \to 0} \int_{0}^{\infty} x^{-\alpha}dx=+\infty [/tex]

But i think the integration limits aren't correct, and therefore [tex] alpha [/tex] is wrong too.

Any help appreciated,

kind regards,

W.

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# Convergence of integral

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