Question

Determine whether this series converges or diverges. If it converges find the sum (see contents of quest for series)

Answer 1

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

Answer 2

Use one of the tests. When in doubt, use ratio test. Always works.

Answer 3

Usually works*

Answer 4

i am not sure of my working. i first split it into partial fractions then took the limit to infinity is that correct?

Answer 5

According to ratio test:
\[L = \lim_{n \rightarrow ∞}\left| \frac{ a_{n+1} }{ a_n } \right|\]
Converges (ans converges absolutely) if L < 1
Diverges if L > 1
Use different test if L = 1

Answer 6

Partial fractions, then it looks as if its telescopic.

Answer 7

partial fractions give me \[\frac{ 1 }{ 2n }-\frac{ 0.5 }{ n+1 }\]

Answer 8

Yes thats it its telescopic. U understand?

Answer 9

no, explain further

Answer 10

AST works on series that alternates between positive and neagtive. is the above series alternating

Answer 11

Converges to 1/2

Answer 12

Understand?

Answer 13

Use comparison to see it converges then do what i did to get the sum

Answer 14

Thx

Answer 15

@Moyo30 understand?

Answer 16

Np

Answer 17

comparison test using which function to compare?

Answer 18

1/n^2

Answer 19

thx, i have to go away. will look @ it when i come back.