State whether the sequence the set of terms with general term, the quotient of the sine of n and the square root of n converges or diverges, and if it converges, give its limit.

Question

State whether the sequence  converges or diverges, and if it converges, give its limit.

A	Diverges
B	Converges to 1 and −1, depending on the value of the numerator
C	Converges to 1
D	Converges to 0

Answer 1

We can wright -1/√n ≤ sinn/√n ≤ 1/√n.

Because lim(-1/√n) = lim(1/√n) = 0 then squize theorem lim sinn/√n = 0

n → ∞ n → ∞ n → ∞

Answer: Converges to 0