Question

I need someone who can help me understand how to solve Series.I have an exam tommorow,so any help would be much appreciated :)

Answer 1

\[\sum_{\infty}^{1}\frac{ n }{ n ^{2} +1}\]

Answer 2

Thank you for calling backup :D

Answer 3

@ayeshaafzal221

Answer 4

do u want to learn basic of series ?

Answer 5

Yes

Answer 6

ok :) give me one minute

Answer 7

Sure ^^

Answer 8

ok so there is two types of series one is infinite which is set of positive numbers and keeps going on theres no stop to it
a1, a2 , a3 ,......
then second type is finite which means limited amount of numbers are in that sequence.

Answer 9

I have to learn the infinite ones

Answer 10

Like the one I posted above

Answer 11

ok can u show me some example of what kind of question you will be getting so i want to know which level u are at , if you dont mind.

Answer 12

Sure

Answer 13

I choose the ones that looked easier for me to understand and put them in that .jpg

Answer 14

I would like to solve them one by one so I can understand them

Answer 15

u know how to take limits right?

Answer 16

kinda

Answer 17

i just learned the basic with another nice guy from this site :D

Answer 18

ok its quite easy basically you take the limit and divide each variable of question with biggest value it ll be mor clear once i solve the question

Answer 19

\[\sum_{\infty}^{1}\frac{ n }{ n ^{2}+1 }\]

Answer 20

i divide with n^2?

Answer 21

yes

Answer 22

but take the limit first like \[\lim_{n \rightarrow \infty} \frac{ n }{ n ^{2} +1}\]

Answer 23

\[\lim_{n \rightarrow \infty }\frac{ \frac{ n }{n ^{2}} }{ \frac{ n ^{2} }{ n ^{2} } +1}\]

Answer 24

like this?

Answer 25

yes :)

Answer 26

And now?

Answer 27

now you cross out the like terms

Answer 28

this might help out
http://www.math.hawaii.edu/~ralph/Classes/242/SeriesConvTests.pdf

Answer 29

If I cross out the like terms,wouldn't it lead me to the exact ecuation with which we started?

Answer 30

no it will be \[\frac{ 0 }{ 1+1 } =0\]

Answer 31

Ohh,I see

Answer 32

I got it

Answer 33

\[\frac{ 0 }{ 1+0 } =0\]

Answer 34

it is infinite/infinite ^ 2 = 0 because infinite ^ 2 is bigger

Answer 35

and infinite ^ 2 / infinite ^ 2 = 1 because it is the same?

Answer 36

yes

Answer 37

do u know what convergent and divergent means?

Answer 38

something that has to do with the result being higher or lower than 1

Answer 39

yes now can u go to this website it has everything you need to know , go through and message me if you dont understand a thing its with examples and solution

Answer 40

http://tutorial.math.lamar.edu/Classes/CalcII/ConvergenceOfSeries.aspx

Answer 41

Thank you :)

Answer 42

dont get scared of first thing scroll down

Answer 43

your welcome :0

Answer 44

:)*

Answer 45

google khan academy geometric series , its a life saver

Answer 46

https://www.khanacademy.org/math/precalculus/seq_induction/infinite-geometric-series/v/infinite-geometric-series

Answer 47

make a free login

Answer 48

I will try to start solve the exercises to see if I can,when I''m stuck I will write the exercise here

Answer 49

Jhanny

Answer 50

You there?

Answer 51

\[\sum_{\infty}^{1}\frac{ n^{2} }{2^{n} }\]

Answer 52

anyone can help me solve this?

Answer 53

put it in a new thread

Answer 54

ok