Need help proving....
Suppose that (an), (bn), and (cn) are sequences such that an≤ bn ≤ cn for all n ɛ N and such that lim an = lim cn = b. Prove that lim bn = b.
Need help proving....
Suppose that (an), (bn), and (cn) are sequences such that an≤ bn ≤ cn for all n ɛ N and such that lim an = lim cn = b. Prove that lim bn = b.
You know that .
For there are so that if we know .
Let . Try to argue that if then by above it must be the case that .
Need help proving....
Suppose that (an), (bn), and (cn) are sequences such that an≤ bn ≤ cn for all n ɛ N and such that lim an = lim cn = b. Prove that lim bn = b.
This is called the squeeze theorem for sequences. The proof is very standard.