1. Write the first five terms of the following sequences: (-1)"n' (i) 2n +1 (ii) (4+ (-1)") (iii) r =1, In1= 3r, +1 (iv) (3,3,3, .)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 6RE
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Dr. Wafa Alqurashi
Introduction to Real Analysis
Exercises (3)
1. Write the first five terms of the following sequences:
2n +1
(ii) (4+(-1)")
(iii) r =1, +=3r, +1
(iv) (3,3,3..)
2. Find the formula of the general n th term In.
(i) (1,3,5,7.)
1 234
(ii)
2 3
11
(iii)
16
3. Which of the following sequences are bounded:
(i) (4)
(ii) (n+)
(iii) (1– )
(iv)
n+1
(A)
4. Use the definition of the limit of a sequence to show that:
2n - 1
(i) lim
(ii) lim(vn+2- Vn+1) 0
3n +1
3
(iii) lim
2n + 5
2
(iv) lim
= 0
n +1
Transcribed Image Text:Dr. Wafa Alqurashi Introduction to Real Analysis Exercises (3) 1. Write the first five terms of the following sequences: 2n +1 (ii) (4+(-1)") (iii) r =1, +=3r, +1 (iv) (3,3,3..) 2. Find the formula of the general n th term In. (i) (1,3,5,7.) 1 234 (ii) 2 3 11 (iii) 16 3. Which of the following sequences are bounded: (i) (4) (ii) (n+) (iii) (1– ) (iv) n+1 (A) 4. Use the definition of the limit of a sequence to show that: 2n - 1 (i) lim (ii) lim(vn+2- Vn+1) 0 3n +1 3 (iii) lim 2n + 5 2 (iv) lim = 0 n +1
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