Recent content by rostbrot

Wow, I can't believe I completely forgot how to use L'Hopital's rule properly... Thanks guys!

...I must be missing something... This is what I've been doing: http://img684.imageshack.us/img684/3658/loglimj.jpg After taking the derivative and simplifying it down I end up with a similar case to what I had before (lines 3 and 9).

lim_{i\rightharpoonup\infty} \frac{ln(4^{i}-1)}{ln(2^{i})} If I set this up right it should go to 2, but I'm pretty rusty and every time I try to work this out I end up getting garbage or repeating behaviors that I can't do anything with... Anyone know what exactly to do with it? edit: Ack...

yeah, I was just kidding about that whole "2" business. The answer is actually 4. And I double checked myself this time. I'm assuming that you were taught that lim as h->0 of f(x) is the format you're used to, right? Here f(x) is not explicitly defined as such but the the fraction which you a...

all you ever do with sequences to find the value they approach is take the limit of it as n -> inf of your general term. when you find the limit of a sequence all you do is take the limit of it. That's it.

sin(h)/h =/ ->1 as h ->1. lim as h-> 1 of sin(h)/h = sin1 I think you're mixing it up with that one fact lim as x -> 0 of sinx/x = 1 or something like that.

Do you have to stick with canceling stuff out algebraically? If not just L'Hopital that sucker. You should get 2.

neither -1/n nor 1/n converge. (-1)^n/n does, however, converge.

Dick, I'm not sure what you're doing up in your previous post, though it may just be the notation... Anyways, I'm in ap calc bc, which is pretty much like calc 2 I guess. I had to get kind of "creative" with it so I don't know if everything I did is exactly legit. So here's my answer...

yes you just treat n as a constant. Be careful when taking the derivative of a series though. Here the issue didn't come up, but if you have x^n where n starts at 0 and end up with x^(n-1) where n starts at 0 then you would get x^(-1) for n=0 which is a no-no so you'd have to move you n up to...

ding ding ding! Because he's so grumpy! hehehe ...

same thing as what Air said, but it just looks so pretty written out! 1______+_______100_= 101 _2_____+______99___= 101 __3____+_____98____= 101 __...___...____...____... ___49__+__52_______= 101 ____50_+_51________= 101 so you got 101 50 times 101x50=5050 so... when summing...