Functional Analysis, spaces [closed]

If p $$\neq$$ q, Show that it implies $$\ell_p$$ $$\neq$$ $$\ell_q$$ $$\\$$

I am new to functional Analysis, I don't know how to go about this.

closed as off-topic by Saad, dantopa, Shailesh, Cesareo, mrtaurhoApr 29 at 8:57

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, dantopa, Shailesh, Cesareo, mrtaurho
If this question can be reworded to fit the rules in the help center, please edit the question.

• Find a sequence $(a_n)$ so that one of $\sum |a_n|^p$ and $\sum |a_n|^q$ is finite and the other infinite. – David Mitra Apr 18 at 12:36
• @DavidMitra Please can you give me an example of one. I have racked my brains, since after you left the comment above. But I couldn't find anything, no headway. Thanks. – Vincent Ebuka Apr 23 at 20:55

Here is another hint: $$\ell_1 \not= \ell_2$$ because $$\sum_{k=1}^\infty \frac 1k = \infty \quad \text{and} \quad \sum_{k=1}^\infty \frac 1{k^2} < \infty.$$ Can you modify this example?