Question

find 10 partial sums of the series, graph sequence of partial sum and sequence of terms, is it convergent or divergent?

Answer 1

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

Answer 2

dang if only I still remember... I do know that there are a lot of tests and each of them have their own unique rules to determine convergent or divergent...

Answer 3

you dont know what test i can use to solve this?

Answer 4

comparison and P-series

Answer 5

1/(n(n+2)) = 1/(n^2 + 2n) < 1/(n^2)

1/n^2 is convergent by P-series, hence 1/(n(n+2)) is convergent by comparison

Answer 6

as far as partial sum goes, just grab a calculator

Answer 7

or use wolfram alpha

Answer 8

i know the answer but since its convergent how would i figure out the answer

Answer 9

well it ask for the 10th partial sum, meaning the sum of the first 10 term. Since n start at 2, the tenth term is n = 11

Answer 10

so i add all the sums?

Answer 11

for the value of the 10th partial so, yes. For the sequence of the partial sums, you need find 1st sum, 2nd sum, ... , 10th sum, and plot those values

Answer 12

10th partial *sum*

Answer 13

i did a table and plot those points, but dont i need another graph?

Answer 14

remember, partial sum isn't the same as the value of the sequence at particular index

Answer 15

geez don't have to be rude... why don't you I don't know just distribute the n on the denominator and use p-series test. any exponent greater than 1 converges . have a nice day *sarcasm*

Answer 16

@sourwing i dont quite understand this?

Answer 17

D:

Answer 18

@UsukiDoll who are you referring with that comment?

Answer 19

you

Answer 20

what graph did you make?

Answer 21

what did i do? @UsukiDoll

Answer 22

you said "you dont know what test i can use to solve this?"

It's been a while for me k... chill and sourwing gave the answer already... use p series it's much easier just distribute the n my gawd!