Answer to Question #113343 in Real Analysis for Awais

Question #113343

Find limit of sequence =n+2/3-n

Expert's answer

Let $(x_n)=\frac{n+2}{3-n}$ be a sequence in $\R$ .

$\therefore \lim_{n\to \infin} (x_n)=lim_{n\to \infin} \frac{n+2}{3-n}$

Divided numerator and denominator by n. We get

lim_{n\to \infin}(x_n)=lim_{n\to \infin} \frac{1+\frac{2}{n}}{\frac{3}{n}-1}

$=\frac{1}{-1}=-1$

Learn more about our help with Assignments: Real Analysis

Comments

No comments. Be the first!

Leave a comment

Related Questions

1. If f(X,y)={xy/x2+y2, if(X,y)#(0,0) 0 if (X,y)=(0,0) Check the con
2. Prove that lim(Xn) =0 iff lim(|Xn|)=0 . Give an example to show that convergence of (|Xn|) need not
3. With the help of sequences, calculate √5 correct upto 5 decimals.
4. Show that if X and Y are sequences such that X and X + Y are convergent, then Y is convergent.
5. Use the order completeness property to show that the set S= {n/n+7:n belong to N} has a supremum and
6. Check whether the function, f , defined below, is uniformly continuous or not: f (x) =x^1/2 , x bel
7. Use Lagrange’s mean value theorem to prove that x-x^2/2<log(1+x)<x-x^2/2(1+x) if x>0