I have the following problem and I am stuck on it. Any ideas on how to work it? Let k be a positive integer. Show that 1^k + 2^k + ... + n^k is O( n^(k+1) )
Follow Math Help Forum on Facebook and Google+
Originally Posted by othnin I have the following problem and I am stuck on it. Any ideas on how to work it? Let k be a positive integer. Show that 1^k + 2^k + ... + n^k is O( n^(k+1) ) You want to show that is bounded as . One way is to write that expression as and think of it as a Riemann sum approximating .
Interesting, I was trying to do a proof by Induction. Do you know if it's possible to it that way? Thanks for heads up!
Originally Posted by othnin I have the following problem and I am stuck on it. Any ideas on how to work it? Let k be a positive integer. Show that 1^k + 2^k + ... + n^k is O( n^(k+1) ) Another way is the following easy one: since for , we have .
Thanks guys. I think I can get a proof out of it now.
View Tag Cloud