Prove {52 + 11/n} n=1 to infinity converges to 52 using the definition of a convergent sequence.

a) Prove that (bn) is also increasing.(b) Suppose that (an) is a convergent sequence. Prove that bn also converges   please explain each step in full detail

2n Using the definition of a convergent sequence, prove lim n+00 3n+1

Prove { (8n-7)/n} n=1 to infinity is an increasing sequence.

Solve the Lucas sequence L_n = L(n-1) + L(n-2), n ≥ 3; L_1 = 1, L_2 = 3.

[sqrt(3n+1)] / [ 2 + sqrt(n)] does this sequence converge? or diverge? and why?

Determine whether the sequence converges or diverges n! An (п + 2)! [ Select ] In(2 + e") 3n

Find the sequence

(3) Suppose {an}_1 is a sequence that converges to 0 and that an 2 0 for all n. Prove {Jan}1 converges to 0 too.

What about the sequence an =16 + (10n2+1)/en for all n.  Is it monotone? Does it converge?  If so, to what?