Question

determine whether the series converges or diverges:

Answer 1

\[\sum_{1}^{\infty} (lnk)/(e ^{\sqrt{k}})\]

Answer 2

0

Answer 3

what test did you use?

Answer 4

when u find the limiting value \[U_{k+1}/U_{n}\]

Answer 5

\[\left| U _{k+1}/U_{k} \right|\]

Answer 6

can you kinda show me how you got zero?

Answer 7

\[ U_{k} = \ln(k)/e^{k} , U_{k+1} = \ln(k+1)/e^{k+1} \]\[ \therefore \left| U_{k+1}/U_{k} \right| = \ln(k+1)/e^{k+1} \times e^{k}/\ln(k)\]

Answer 8

\[ \ln(1) \times e^{\sqrt(k)-\sqrt(k+1)} = 0\]

Answer 9

did that help ?

Answer 10

great! thanks :)

Answer 11

what was the answer in the text book ?

Answer 12

it wasn't from my textbook so i don't know the right answer but that looks right.