Absolute convergent, conditionally convergent or divergent, Mathematics

Assignment Help:

Find out if each of the subsequent series are absolute convergent, conditionally convergent or divergent.

185_Absolute convergent, Conditionally convergent or Divergent.png

Solution:

(a)

1815_Absolute convergent, Conditionally convergent or Divergent 1.png

The above is the alternating harmonic series and we saw in the previous section that it is a convergent series so we there is no requirement to check that here.  Thus, let's see if it is an absolutely convergent series.  To do this we will need to check the convergence of.

1402_Absolute convergent, Conditionally convergent or Divergent 2.png

 

This is harmonic series and we were familiar from the integral test part that it is divergent. Hence, this series is not absolutely convergent.  Though, It is conditionally convergent as the series itself does converge.

(b) 

2279_Absolute convergent, Conditionally convergent or Divergent 3.png

In this example let's just test absolute convergence first as if it's absolutely convergent we won't need to difficulty checking convergence as we will get that for free.

761_Absolute convergent, Conditionally convergent or Divergent 4.png

This type of series is convergent by the p-series test and thus the series is absolute convergent. 

Note: This does say as well that it is a convergent series.


Related Discussions:- Absolute convergent, conditionally convergent or divergent

Pre Calculus, I have no idea how to graph exponential forms.

I have no idea how to graph exponential forms.

Limits at infinity part ii, Limits At Infinity, Part II :  In this sectio...

Limits At Infinity, Part II :  In this section we desire to take a look at some other kinds of functions that frequently show up in limits at infinity.  The functions we'll be di

Determine the conditional probability, Consider a class of 55 students. The...

Consider a class of 55 students. The student names are placed in a hat and 3 names are randomly drawn without replacement. a) If the first person drawn was named the class presi

#i need help on my math homework its on algabraitle.., The question is: If ...

The question is: If 0.2 x n = 1.4,what is the value of n.

Recognizes the absolute extrema & relative extrema, Recognizes the absolute...

Recognizes the absolute extrema & relative extrema for the following function.                           f ( x ) = x 2       on [-1, 2] Solution:  As this function is simpl

George worked from 7:00 am to 3:30 pm how much he earn, George worked from ...

George worked from 7:00 A.M. to 3:30 P.M. with a 45-minute break. If George earns $10.50 per hour and does not obtain paid for his breaks, how much will he earn? (Round to the near

Trigonometry, If sec A = x+i/x, prove that sec A + tan A = 2x or 1/2x

If sec A = x+i/x, prove that sec A + tan A = 2x or 1/2x

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd