- #1
- 4,807
- 32
Apparently (according to my textbook), the sequence defined by
[tex]\left\{\frac{1}{n^2}+\frac{2}{n^2}+...+\frac{n-1}{n^2}\right\}[/tex]
converges towards 1/2, i.e. has 1/2 as a limit.
How could that be?! It seems to me that as n approaches infinity, all the fractions fall to zero. What is it I'm missing?
[tex]\left\{\frac{1}{n^2}+\frac{2}{n^2}+...+\frac{n-1}{n^2}\right\}[/tex]
converges towards 1/2, i.e. has 1/2 as a limit.
How could that be?! It seems to me that as n approaches infinity, all the fractions fall to zero. What is it I'm missing?