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ƒ(x)
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If n is a positive integer, then the limit of [tex]\sum k/n^2[/tex] from k=1 to n as n approaches infinity = ?
A) pi
B) 1
C) 1/2
D) 1/pi
E) 0
How do I do this?
A) pi
B) 1
C) 1/2
D) 1/pi
E) 0
How do I do this?
payumooli said:c) 1/2
since 1/n^2 is constant remove it outside
sum of n natural numbers formula can be used for the summation
then you have lim tending to infinity
n(n+1)/(2n^2)
use L 'opital
should be right
LCKurtz said:Yes, of course. That's why I said "technically". Still, I think it is best if students learn to use the more elementary methods when they are appropriate.
ƒ(x) said:Thanks, the answer is C. But, is there another way to do this?
The limit of the series
The value of the series
When a series has a limit as n approaches infinity, it means that as n gets larger and larger, the terms in the series approach a specific value. This can be a finite number, infinity, or negative infinity. In the case of
No, the limit of
The series