Question

How to apply sqeeze theorem in sequence?

Answer 1

suppose we want to show that {a(n)} = e^-(n+sin(n) ) approaches 0 as n -> inf
well suppose we define some b(n) = e^-(2n), it can be seen that for all natural number n, b(n) < a(n) therefore {b(n)} < {a(n)}.
Similarly c(n) = e^-(n/2), a(n) < c(n), so {b(n)} < {a(n)} < {b(n)}.
n -> inf for {b(n)} = {c(n)} = 0, so by the squeeze theorem {a(n)} approaches 0.

Answer 2

i meant "{b(n)} < {a(n)} < {c(n)}"