(a) If {an} is convergent, show that limn →∞ an+1=limn →∞ an (b) A sequence {an} is defined by a

Name: Problem 76, Chapter 11: Calculus: Early Transcendentals
Uploaded: 2022-11-10T12:44:18-08:00
Duration: 3 min 45 s
Channel: Khoobchandra Agrawal
Description: (a) If {an} is convergent, show that limn →∞ an+1=limn →∞ an (b) A sequence {an} is defined by a1=1 and an+1=1 /(1+an) for n ⩾1. Assuming that {an} is convergent, find its limit.

step 1 First part, let limit n tending to infinity nth term is l. It means that for every element to be

(a) If {an} is convergent, show that limn →∞ an+1=limn →∞ an...

(a) If $\left\{a_n\right\}$ is convergent, show that $$ \lim _{n \rightarrow \infty} a_{n+1}=\lim _{n \rightarrow \infty} a_n $$ (b) A sequence $\left\{a_n\right\}$ is defined by $a_1=1$ and $a_{n+1}=1 /\left(1+a_n\right)$ for $n \geqslant 1$. Assuming that $\left\{a_n\right\}$ is convergent, find its limit.

(a) If $\left\{a_n\right\}$ is convergent, show that

$$
\lim _{n \rightarrow \infty} a_{n+1}=\lim _{n \rightarrow \infty} a_n
$$

(b) A sequence $\left\{a_n\right\}$ is defined by $a_1=1$ and $a_{n+1}=1 /\left(1+a_n\right)$ for $n \geqslant 1$. Assuming that $\left\{a_n\right\}$ is convergent, find its limit.