## privetek 2 years ago determine whether the series converges or diverges:

1. privetek

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

2. EarthCitizen

0

3. privetek

what test did you use?

4. EarthCitizen

when u find the limiting value $U_{k+1}/U_{n}$

5. EarthCitizen

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

6. privetek

can you kinda show me how you got zero?

7. EarthCitizen

$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)$

8. EarthCitizen

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

9. EarthCitizen

did that help ?

10. privetek

great! thanks :)

11. EarthCitizen

what was the answer in the text book ?

12. privetek

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