Help With Algorithms!

[KidViciou$]

i need ot show that the sum for k running from 1 to n of (lg k)/k is Theta((lg k)^2) by bounding the individual terms.

basically i don't know what they mean by bounding the individual terms. i already proved it by integration

TIA!!!

 

[stnicralisk]

Since passing Calc 2 I have taken such challenging courses as Trig. and Geometry and it has rotted my brain. Can we prove it is true by construction? Is there a picture involved? Scan the problem in and we can solve it with only a straight edge and compass. (I had to move backwards so I can teach Secondary Math and honestly I can barely remember anything but triangles now... I think theyre taking over the world.)

 

[KidViciou$]

There is no problem in a book, nor a picture. there should be no need for any measuring device as this is a purely mathematical problem:


# Show that the sum, for k running from 1 to n, of (lg k) / k , is Theta ( lg2 k ), in two ways:

1. by integration, and
2. by bounding the individual terms (this is tricky!)

(Hint: you might use the very useful result (A.7)).



it's not Theta(lg2... on the original website, he had is superscripted, but i can't do that here

 

[KidViciou$]

^to the top

 

[DrPizza]

and, what is the result of A.7?