Question

k=1 sigma K tends to infinity (k+1)/(k+2) this series is converges or diverges../

Answer 1

Um...put some numbers in for k...

Answer 2

put the number then..? how can i identify this series is diverges or converges

Answer 3

Inspection...(by eye).

Try k=1, 10,100, 1000

Answer 4

this series is telescopoing..?

Answer 5

suppost i put 1 the result is 2/3 how can i identify the series 2/3 is diverges or converges..?

Answer 6

2/3 is not a series....

Answer 7

can u explain now plz for this series..?

Answer 8

Your series is for values ok from 1 to infinity (although infinity is not actually a value).

In other words what happens to your expression as k increases without limit?

As u say, with k = 1, your expression is 2/3 but when k is 10 then it is 11/12 and when it is 100 then it is 101/102 and so on....

If I use decimals instead of fractions:

0.666666....
0.9166666....
0.999196...

Answer 9

then

Answer 10

?

Answer 11

series is converges or diverges..? can u know..?

Answer 12

Did you read my post?

Answer 13

yes... but i cant undersstnd what u say..?

Answer 14

Which part?

Answer 15

how can i identify ...?

Answer 16

As k increases, what happens to the value of the expression?

Answer 17

value increses.

Answer 18

bro we use the ratio test? for identify the series converges or diverges..?

Answer 19

The value increases.... with or without a limit?

Answer 20

yes

Answer 21

Yes, what?

Answer 22

i cant what u say... i cant understand .. u r understnading style is very chep

Answer 23

U said the value increases....

How big does it get?

Answer 24

u ask me qus qus qus i told i cant understnd plz explain now but u again and again ask the qus.

Answer 25

yup definitly i told u value is increse..

Answer 26

k=1 -> 2/3
k = 10 ->11/12
k = 100 -> 101/102
k = 1000 -> 1001/1002
k = 10000 -> 10001/10002

Can u see?

Answer 27

yes i see

Answer 28

OK, what do you see?

Answer 29

value is dicreases.?

Answer 30

The value is getting closer and closer to 1

Answer 31

yup so series is diverges.?

Answer 32

Convergent means to come to a limit, divergent means there is no limit.

Here the limit is 1.

Answer 33

use the divergence test show that the series is diverges this is my real qus

Answer 34

U mean convergence test, there is no need in this case, the answer is obvious.

Answer 35

why dont need in this case../

Answer 36

What is 1+1+1+1+1+..........?

Answer 37

i dont kniw

Answer 38

Infinite, right? As big as you want to keep adding more 1's.

Basically, that is your question, you have an infinite number of terms that are nearly 1 so the sum of all those terms is infinite.

Answer 39

oka

Answer 40

So your sum diverges....

Answer 41

1/1+6

Answer 42

divergs or convetgs

Answer 43

??

Answer 44

same qus but value is chagen

Answer 45

http://en.wikipedia.org/wiki/Series_%28mathematics%29

Answer 46

i also know this site..

Answer 47

All the explanation and tests are mentioned there....