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

1. anonymous

$\sum_{\infty}^{1}\frac{ n }{ n ^{2} +1}$

2. anonymous

Thank you for calling backup :D

3. anonymous

@ayeshaafzal221

4. anonymous

do u want to learn basic of series ?

5. anonymous

Yes

6. anonymous

ok :) give me one minute

7. anonymous

Sure ^^

8. anonymous

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.

9. anonymous

I have to learn the infinite ones

10. anonymous

Like the one I posted above

11. anonymous

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.

12. anonymous

Sure

13. anonymous

14. anonymous

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

15. anonymous

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

16. anonymous

u know how to take limits right?

17. anonymous

kinda

18. anonymous

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

19. anonymous

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

20. anonymous

$\sum_{\infty}^{1}\frac{ n }{ n ^{2}+1 }$

21. anonymous

i divide with n^2?

22. anonymous

yes

23. anonymous

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

24. anonymous

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

25. anonymous

like this?

26. anonymous

yes :)

27. anonymous

And now?

28. anonymous

now you cross out the like terms

29. IrishBoy123

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

30. anonymous

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

31. anonymous

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

32. anonymous

Ohh,I see

33. anonymous

I got it

34. anonymous

$\frac{ 0 }{ 1+0 } =0$

35. anonymous

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

36. anonymous

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

37. anonymous

yes

38. anonymous

do u know what convergent and divergent means?

39. anonymous

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

40. anonymous

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

41. anonymous
42. anonymous

Thank you :)

43. anonymous

dont get scared of first thing scroll down

44. anonymous

45. anonymous

:)*

46. anonymous

47. anonymous
48. anonymous

49. anonymous

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

50. anonymous

Jhanny

51. anonymous

You there?

52. anonymous

$\sum_{\infty}^{1}\frac{ n^{2} }{2^{n} }$

53. anonymous

anyone can help me solve this?

54. IrishBoy123

put it in a new thread

55. anonymous

ok