Question

Help me with finding the limit of this sequence-

Answer 1

\[\lim_{? \rightarrow \infty} n \sin(1/n)\]

Answer 2

is it as n approaches infinity?

Answer 3

Yeap!

Answer 4

\[\lim_{n \rightarrow \infty} nsin(1/n)\]

Answer 5

Let n = 1/x
\[\implies \lim_{n\rightarrow \infty} nsin(1/n) = \lim_{x\rightarrow0} \frac{sin(x)}{x}\]

Answer 6

Oh, 1 is the answer then.......

Answer 7

very nice :)

Answer 8

Another one- \[\lim_{n \rightarrow \infty} (n!)^{2}/(2n)!\]