Question

anybody good at calculus 2 ? i need help D:

Answer 1

I am here

Answer 2

sweet! how r u at series? lol

Answer 3

shoot some questions

Answer 4

okay well im a little bit confused about the alternating series test, how do you knw when to apply it, and do you combine it with other test as well to show that its either absolutely convergent or conditionally convergent?

Answer 5

i can tell you simply that if the series alternates, the sum will converge if the terms go to zero, so it is usually very easy to check

Answer 6

for example
\[\sum\frac{1}{k}\] diverges but
\[\sum\frac{(-1)^k}{k}\] converges

Answer 7

is that absolute or conditional convergence?

Answer 8

i did the ast i used the derivative i got -1/K^2 with is <0 then i used the limit and it converges towards zero

Answer 9

i knw that it converges by the alternating series test, am i done over all? or do i have to use another test to show that it converges absolutely or converges conditionally, cuz if u use the lct it would diverge cuz ur bn that ur comparing it with is 1/k which is a harmonic series and that converges

Answer 10

what was the original problem?

Answer 11

(-1)^k/K

Answer 12

oh just the one i wrote!!

Answer 13

ok you need no real tests for this

\[\lim_{k \to \infty}\frac{1}{k}=0\] so alternating series converges

Answer 14

no my bad harmonic series diverges! not converge lol

Answer 15

however harmonic series diverges, so this clearly does not converge absolutely because it the absolute value gives the harmonic series

Answer 16

to recap:
terms go to zero, alternating series converges
abosolute value is harmonic series, diverges, so not absolutely convegent

Answer 17

so... do alternating series stop at the showing that it is <0 and finding the limit or do you have to continue to show the overall answer such as absolutely converges or converges conditionally

Answer 18

converging "conditionally" means not absolutely convergent.

Answer 19

i really am not sure what you are asking. all you need is that the terms to go zero

Answer 20

what does "it is <0 " mean?

Answer 21

it means that the first step in using the alternating series test is to prove that an+1is less than an either using the derivative, or an+1/an is less than 1 or an+1-an greater than zero to show that an+1 is always less that an