Question

f

Answer 1

i will try to type it better

Answer 2

Well do you know the alternating series convergence test?

Answer 3

i do not

Answer 4

i know it has something to do with the abs value i think

Answer 5

Well the ALT test states, that for\[\sum_{k=M}^\infty(-1)^k a_k\]If the three following conditions are met, then the sum converges:
\[a_{k+1}<a_k\]\[a_k>0\]\[\lim_{k\rightarrow\infty}a_k =0\]

Answer 6

what is m?

Answer 7

i dont think it converges

Answer 8

M stands for any positive integer. You could have it be 10000000 - the point is, everything summed up before it has to come to a finite sum. The point is that after M you will always follow the three rules.

Answer 9

@daniellerner why not?

Answer 10

isnt part one saying it doesnt

Answer 11

not really. But let's see:
\[\frac{ln(k)}{ln(k+k^2)}>\frac{ln(k+1)}{ln(k+1+(k+1)^2)}\]

Answer 12

Do you not see that the denominator grows faster than the numerator?

Answer 13

oh yeah i see that

Answer 14

well as for the last one, you might want to use L'H rule.

Answer 15

and for the last one you get 0

Answer 16

well then, you're set!

Answer 17

so is it conditoinally or absolutely converges?

Answer 18

can you check my work so far to see if thats right

Answer 19

no we only proved conditionally so far. Your 'work' should be using the L'H rule and the limit that you get from it.

Answer 20

do you want me to type my work out here?

Answer 21

Well that depends on whether you feel like it needs to be revised.

Answer 22

id use ratio test for checking absolute convergence.

Answer 23

ok