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Help needed with an integration and limits problem! watch

1. Hi there guys,
I'm stuck on this problem at uni involving limits and integrals. Any help would be greatly appreciated, and a step by step solution would be even better.

Many thanks in advance,
Kitrak

BTW, the question is attached as an image

2. integrate x^(-a) as you would normally. then think about for which values of a the integrated function makes sense.

Hint:
Spoiler:
Show
a>1
3. i don't understand, sorry.
4. I mean, once i integrate, what do i do from there?
5. any help?
6. This seems a very interesting question, would love to see an answer to this.
7. any help guys?!
8. When a = 2 we have,

so the integral converges in this case
Try it for other values of a (say 0.5, 1) at see what happens
Then try a more general proof
9. what type of general proof do i then do?
10. any ideas guys?
11. Can you find ?
12. Remember, you have your bog standard rule:

(or, in words, add one to the power, then divide by the power.)

Now, can you apply this rule to ?

Once you've found this, plug in the limits of integration, N and 1.

Finally, find the values of a for which your answer doesn't -> infinity when N -> infinity.

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