Answer to Question #179059 in Algebra for Anuj

Question

Let(a↓n) ↓n€B be any sequence. Show that lim↓n-->♾️ a↓n =Liff for every E>0, there exists some N€N such that n>=N implies a↓n N↓e (L)

Answer 1

Prove that {an} is a Cauchy sequence. Solution . First we prove by induction on n that |an+1 − an| ≤ αn−1|a2 − a1| for all ...

an < A + ε. 2. , and there exists N2 such that for all n>N2, bn < B + ε. 2 . But then if N = max(N1, N2), then for any n>N we have an + bn < A + .

..xn − 1,n ∈ N. Show that (xn) is decreasing and bounded below by 2. Find the ... 2 + xn,n ∈ N. Show (xn) converges and find the limit. ... 2+2 = 4, so xn < 2 for all n ∈ N by induction