The problem involves finding the limit of the sum \( \frac{1}{n^2} + \frac{2}{n^2} + \frac{3}{n^2} + \ldots + \frac{n-1}{n^2} \) as \( n \) approaches infinity, which falls under the topic of limits and series in calculus.
The discussion is active, with participants sharing their reasoning and attempting to clarify concepts. Some guidance has been provided regarding the summation formula for arithmetic series, and there is an ongoing exploration of the implications of this formula for the limit.
There is some confusion regarding the terminology used, particularly around "closed form" and the nature of the series (arithmetic vs. geometric). Participants are also navigating the correctness of their approaches and interpretations of previous contributions.
sara_87 said:Homework Statement
find:
lim(n[tex]\rightarrow\infty[/tex] (1/n^2 + 2/n^2 + 3/n^2 + ... + n-1/n^2 )
Homework Equations
3. The Attempt at a Solution [/b
I could guess that the limit is zero but i don't know howto prove it
sara_87 said:I have done it and i just want to make sure of my answer:
i used the summation formula for aritmetic series :1/2 n(n+1)
and got that the limit is 1/2
is that right?
Dick said:BTW, I didn't say anything before in this thread. That was Halls. Let's give credit where credit is due.
Mark44 said:Sorry for giving credit where not due. I think I saw your name in another thread that sara started, and mistakenly cited you and Dirk.