Expert: Paul Klarreich - 5/1/2009

Question
Find the limit as n approaches infinty
An = 1/n2 + 2/n2 + 3/n2 + … + n/n2

Answer
Questioner:   Michael Tadesse
Country:  Ethiopia
Category:  Calculus
Private:  No
 
Subject:  Calculus
Question:  Find the limit as n approaches infinty
An = 1/n2 + 2/n2 + 3/n2 + … + n/n2
..........................
Hi, Michael,

I assume you mean:
               k
SUM(k=1 to n) ----
              n^2

Now you can use this formula:
                 n(n+1)
SUM(k=1 to n) k = ------
                   2
and note that in:

               k
SUM(k=1 to n) ----
              n^2

the 'n' is a constant so we can write:


SUM(k=1 to n) k    n(n + 1)    
---------------- = ---------
    n^2              n^2

I think you can handle it from here.