# Thread: the next part of the norm question..

1. ## the next part of the norm question..

http://i37.tinypic.com/2nhosqa.jpg

i tried:
$
x_i=\frac{1}{i^s}
$

i from 1 to infinty
the whole sum is called u
$
\left \| u \right \|_p=(\sum_{n=1}^{\infty}(\frac{1}{i^s})^p)^\frac{ 1}{p}$

and i think we need to show that i converges

but thats only a shot in the dark

i dont have a clue about it

2. Yes that's what you had to do.

Now, recall that $(a^b)^c=a^{bc}$ to get $\left(\frac{1}{i^s}\right)^p=\frac{1}{i^{sp}}$

For what s (depending on p) does $\sum_{i=1}^\infty \frac{1}{i^{sp}}$ converge ?

It's just a Riemann sum...

And taking something to the power 1/p doesn't change anything in the convergence or divergence.