Femtobytes
Problem type

Limit of a sequence from the definition

What it solves
Prove that a sequence of the form (an + b) / (cn + d) converges to its limit, using only the definition of convergence: for every tolerance epsilon, find the position M after which every term is within epsilon of the limit.
Subject
Real Analysis
Topic
Limits from the definition
Also called
epsilon N, convergence of a sequence, sequence converges, limit of a sequence
Your problem

Prove this limit using only the definition of convergence, then try the proof out with the tolerance ε=110\varepsilon = \frac{1}{10}.

lim⁡n→∞3n+12n−5=32\lim_{n \to \infty} \frac{3 n + 1}{2 n - 5} = \frac{3}{2}
Invent a new one: