What Is the Limit of n*sin(1/n^2) as n Approaches Infinity?

[dickshant]

Hello, can anyone help me with these questions... At least one of them please... thank you

1 Find the limit as → ∞, if it exists, of:(i) √︀( ( + 1)) − 2 , (ii) sin(1/(^2))
I really cannot understand how to do this...thanks for your help:):)

 

[HallsofIvy]

You seem to be using a number of "special symbols". All my viewer shows is a square for each.

 

[dickshant]

ok...i will reformulate the question
find the limit as n tends to infinity, if it exists of
1. root(n(n+1))-2n

2. n*sin(1/n^2)
Thanks...:)

 

[Bohrok]

For the first one, multiply out what you have in the square root and pull out n² from the square root.
For the second, you might try the substitution u = 1/n