Sample --A-Q: Test the series converges, diverges, absolutely converges orconditionally converges:1) Σ=112√n+ ³√n

Answered: Image /qna-images/answer/ca663d42-d5fe-48c0-b684-f22dc321b834.jpg

Answered: Sample-A- Q: Test the series converges,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Sample --A-
Q: Test the series converges, diverges, absolutely converges or
conditionally converges:
1) Σ=1
1
2√n+ ³√n

Expert Solution

Step 1: Step 1

$W e space h a v e space t h e space f o l l o w i n g space s e r i e s sum from n equals 1 to infinity of fraction numerator 1 over denominator 2 square root of n plus cube root of n end fraction F o r space a l l space n space i n space straight natural numbers square root of n greater or equal than cube root of n 3 square root of n greater or equal than 2 square root of n plus cube root of n fraction numerator 1 over denominator 2 square root of n plus cube root of n end fraction greater or equal than fraction numerator 1 over denominator 3 square root of n end fraction$