Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I have to show that the function

[tex]f(x) = \sum_{n=1}^{\infty}\frac1{x^2+n^2}[/tex]

tends to 0 as [tex]x \rightarrow \infty[/tex], i.e. [tex]\lim_{x\rightarrow\infty}f(x) = 0[/tex]. How can I do this?

There is a hint that says I should use the inequality [tex] f(x) \leq \sum_{n=1}^N\tfrac1{x^2+n^2} + \sum_{n=N+1}^\infty\tfrac1{n^2} [/tex]. It is obvious that the first term approaches 0 as [tex]x \rightarrow \infty[/tex], but what about the second term?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Math problem (analysis)

**Physics Forums | Science Articles, Homework Help, Discussion**