So if we let x>0, For which 0<p<=infinity is {1/n^x} an element of l^p?(adsbygoogle = window.adsbygoogle || []).push({});

If x=1, then 1/n^x is clearly an element of l^p for p>=2, since for all these vector spaces, the series of 1/n will converge?

But if x<1, then in it seems that only for p=infinity, will {1/n^x} be an element of l^p. Is this correct?

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

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!

# Question about vector space l^p

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