privetek
determine whether the series converges:
sum(k=1 -> infinity) [1/(1+lnk)]
Delete
Share
This Question is Closed
amistre64
Best Response
You've already chosen the best response.
0
what the limit of lnk as k to inf?
slaaibak
Best Response
You've already chosen the best response.
0
even if the n'th term tends to 0, it doesn't say the series converges.
amistre64
Best Response
You've already chosen the best response.
0
yeah, was thinking thru the convergence tests :)
slaaibak
Best Response
You've already chosen the best response.
0
harmonic series as an example.
amistre64
Best Response
You've already chosen the best response.
0
does 1+ln(x) drop faster than x tho?
amistre64
Best Response
You've already chosen the best response.
0
might need to use a comparison test
privetek
Best Response
You've already chosen the best response.
0
yes, that's what i was thinking..
i got -- 1/(1+lnk) > 1/lnk
and i don't know where to go from here or this is even right..
slaaibak
Best Response
You've already chosen the best response.
0
it's the other way around.
1/lnk > 1/(1+ lnk)
so if you can determine whether 1/ln k converges, you can say /1(1+lnk) converges. but if 1/lnk diverges, you can't say anything about 1/(1+lnk)
Algebraic!
Best Response
You've already chosen the best response.
1
just use 1/k as a comparison
privetek
Best Response
You've already chosen the best response.
0
would 1/k be less than 1/1+lnk ?
Algebraic!
Best Response
You've already chosen the best response.
1
yes
Algebraic!
Best Response
You've already chosen the best response.
1
that's the point
privetek
Best Response
You've already chosen the best response.
0
great, thanks!! :)
Algebraic!
Best Response
You've already chosen the best response.
1
sure:)