Que 3.3. Test the following series for co 1 i. 1.2.3 2.3.4 3.4.5 1 ii. 1+ 22 33 22 33 44

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 49E
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Question
test the following series of convergence
Que 3.2.
en
1+2+3+ ... + n+.... 00
. 00
1.
ii. 5-4-1+5-4-1+5-4-1+.... o
Answer
n(n+1)
8, 1+2+3+ ..... + n =
2
Here,
lim
%3D
2 n
8. = 5 – 4 –1 + 5 – 4 – 1 + 5 – 4-14
0,5 or 1
ii. Here,
*.n ter
%3D
is oscillatory.
Test the following series for convergene
Que 3.3.
3
i.
1.2.3 2.3.4
3.4.5
22 33
ii.
1+
+ ... 00
2 33 44
Answer
i.
We have u
2n - 1
1
2-1/n
%3D
n(n + 1)(n + 2)
Taking v, = 1/n², we have
n2 (1+1/n)(1+2/
%3D
:lim
u.
lim
2-1/n
2-0
(1+1/n)(1+ 2/ n) (1+0X1+
2, which is finite and non zero.
n
%3D
Hend
Transcribed Image Text:Que 3.2. en 1+2+3+ ... + n+.... 00 . 00 1. ii. 5-4-1+5-4-1+5-4-1+.... o Answer n(n+1) 8, 1+2+3+ ..... + n = 2 Here, lim %3D 2 n 8. = 5 – 4 –1 + 5 – 4 – 1 + 5 – 4-14 0,5 or 1 ii. Here, *.n ter %3D is oscillatory. Test the following series for convergene Que 3.3. 3 i. 1.2.3 2.3.4 3.4.5 22 33 ii. 1+ + ... 00 2 33 44 Answer i. We have u 2n - 1 1 2-1/n %3D n(n + 1)(n + 2) Taking v, = 1/n², we have n2 (1+1/n)(1+2/ %3D :lim u. lim 2-1/n 2-0 (1+1/n)(1+ 2/ n) (1+0X1+ 2, which is finite and non zero. n %3D Hend
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