Question

(4) Let \( x_{n}=\frac{1}{\ln (n+1)} \) for \( n \in \mathbb{N} \). (a) Use the Definition 5.3 to show that \( \left(x_{n}\right) \) converges to 0 . (b) Find a specific value of \( N \in \mathbb{N} \) as required in the formal definition of limit for each of (i) \( \varepsilon=\frac{1}{2} \) and (ii) \( \varepsilon=\frac{1}{10} \).

          (4) Let \( x_{n}=\frac{1}{\ln (n+1)} \) for \( n \in \mathbb{N} \).
(a) Use the Definition 5.3 to show that \( \left(x_{n}\right) \) converges to 0 .
(b) Find a specific value of \( N \in \mathbb{N} \) as required in the formal definition of limit for each of (i) \( \varepsilon=\frac{1}{2} \) and (ii) \( \varepsilon=\frac{1}{10} \).

(4) Let xn=(1)/(ln (n+1)) for n ∈ℕ.
(a) Use the Definition 5.3 to show that (xn) converges to 0 .
(b) Find a specific value of N ∈ℕ as required in the formal definition of limit for each of (i) ε=(1)/(2) and (ii) ε=(1)/(10).

Added by Kim B.

Calculus: Early Transcendental Functions

Robert T. Smith, Roland B. Minton 3rd Edition

Chapter 8

Instant Answer

Solved by Expert Linh Vu

09/15/2020

Step 1

3, a sequence \( (x_{n}) \) converges to a limit \( L \) if for every \( \varepsilon > 0 \), there exists a natural number \( N \) such that for all \( n \geq N \), \( |x_{n} - L| < \varepsilon \). We want to show that \( (x_{n}) \) converges to 0, so we want to Show more…

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