There is no delta in the definition of convergence for a sequence that converges to a finite number. So for a sequence {an} that converges to L, the definition says that there is some number N such that |an - L| < epsilon, for all n >= N.harmonie_ post: 2919712 said:Homework Statement
hey there I have been given a question that asks me to define a sequence Xn which tends to infinity that has a limit that is infinity! I am so cofused. I would assume to use an adapted version of the epsilon delta condition?
Homework Equations
It's for Analysis!
The Attempt at a Solution
I attempted :
For all E > 0, there exists a delta >0 s.t. 0<!x!<delta then ?
Thanks!
The formal definition of a sequence limit which tends to infinity is that for any real number M, there exists a natural number N such that for all n greater than N, the value of the sequence is greater than M.
The limit of a sequence that tends to infinity is written as lim n→∞ an = ∞, where an is the sequence and ∞ represents infinity.
For a sequence to tend to infinity means that the terms of the sequence are increasing without bound, becoming larger and larger without any limit.
No, a sequence cannot have a limit that tends to infinity. The limit of a sequence must be a real number or undefined. If the limit of a sequence tends to infinity, then it is said to not exist.
The concept of a sequence limit that tends to infinity is used in many areas of mathematics, including calculus, real analysis, and number theory. It is often used to prove the convergence or divergence of a sequence, and to understand the behavior of functions and series as the input approaches infinity.