Determine series is convergent or divergent by radio test, Mathematics

Assignment Help:

Determine if the following series is convergent or divergent by using Radio Test.

171_Determine series is convergent or divergent by Radio Test 1.png

Solution

With this first illustration let's be a little careful and ensure that we have everything down correctly.  Now Here are the series terms an.

an = (-10)n/42n+1 (n+1)

Remind that to compute an+1 all that there is a requirement to do is substitute n+1 for all the n's in an.

an+1 = (-10)n+1/ 42(n+1)+1 ((n+1)+1

= (-10)n+1/ 42n+3 (n+2)

Now, to illustrate L we will use,

1236_Determine series is convergent or divergent by Radio Test 2.png

As this will be a little easier while dealing with fractions like we've got here.  Thus,

1508_Determine series is convergent or divergent by Radio Test 3.png

Thus, L<1 and so by the Ratio Test the series converges absolutely and therefore will converge.


Related Discussions:- Determine series is convergent or divergent by radio test

Addition and subtraction, In addition and subtraction we have discussed ...

In addition and subtraction we have discussed 1) Some ways of conveying the meaning of the operations of addition and subtraction to children. 2) The different models o

Mathematical model representing the total parking cost, John has a choice o...

John has a choice of using one of two parking garages when he visits downtown: Option1:  $8 an hour for the first two hours, then $2 and hour for each hour more than 2; or Op

Minimizing the sum of two distances, The value of y that minimizes the sum ...

The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a+b.

base - 10 block math, there are 5 small cubes and it reads the 5 small cub...

there are 5 small cubes and it reads the 5 small cubes is 1/100, then what is the ONE?

Shares and dividends, How do I proceed with a project on Shares and Dividen...

How do I proceed with a project on Shares and Dividends?

Applications of derivatives, Applications of derivatives : At last, let's ...

Applications of derivatives : At last, let's not forget about our applications of derivatives. Example    Assume that the amount of air in a balloon at any time t is specified

Monotonic, Monotonic, Upper bound and lower bound Given any sequence {a...

Monotonic, Upper bound and lower bound Given any sequence {a n } we have the following terminology: 1.   We call or denote the sequence increasing if a n n+1 for every n.

Differential equations, Verify Liouville''''s formula for y "-y" - y'''' + ...

Verify Liouville''''s formula for y "-y" - y'''' + y = 0 in (0, 1) ?

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