Real Analysis IIProve whether the series converges or divergesPlease adhere to example in other photo 8]Tj=1(23) 2! controlRatio TestOntic(W)0016im2200 2245lox209-02 Root testGJaj(im Sup (21+2)! . (31) != (in Sup (231 + 2) 23;+) (23;)! 5 !(સુ) .(૩) (28+2)2;+)(2;)! 5!(3; +3)(3+2)X(3; + √(5₂)! (;)."(2j)!Lafio testtim sup lakLim Sup |ax| ³K > 1тукisTajtiCum sup ajlim inf faithKaj saj|[2G +0] !study linsup [3 (+]!=rojow412+1(j+()!Lim Sup 13/10412riK²1 ak Conv.div.ак2K&T(2)!(33)!j²1ajaj Conv.div.jHTim sup (5+1)! 2³= Lim Sup C= Lim Sup 2/j+1=0 21→ Series Cond.

Using the ratio test, it can be written that ∑j=1∞aj converges, if limsup aj+1aj<1 and ∑j=1∞aj…

Answered: j=1 (2³) ² j!

Math

Advanced Math

j=1 (2³) ² j!

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.4: Values Of The Trigonometric Functions

Problem 21E

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Question

Real Analysis II Prove whether the series converges or diverges Please adhere to example in other photo

control
Ratio Test
Ontic
(W)
0016
im
2200 2245
lox2
09-02 Root test
G
Jaj
(im Sup (21+2)! . (31) != (in Sup (231 + 2) 23;+) (23;)! 5 !
(સુ) .(૩) (28+2)2;+)(2;)! 5!
(3; +3)(3+2)X(3; + √(5₂)! (;)."
(2j)!
Lafio test
tim sup lak
Lim Sup |ax| ³K > 1
тук
is
Tajti
Cum sup aj
lim inf faith
Kaj saj
|[2G +0] !
study linsup [3 (+]!=
rojow
41
2+1
(j+()!
Lim Sup 13/1
041
2
ri
K²1 ak Conv.
div.
ак
2
K&T
(2)!
(33)!
j²1
aj
aj Conv.
div.
jH
Tim sup (5+1)! 2³
= Lim Sup C
= Lim Sup 2/j+1=0 21
→ Series Cond.

Branch of mathematical analysis that studies real numbers, sequences, and series of real numbers and real functions. The concepts of real analysis underpin calculus and its application to it. It also includes limits, convergence, continuity, and measure theory.

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