Recent content by silvermane

Yeah I just recently realized that it wouldn't work. That explains why I wasn't understanding how to apply my reasoning to the right-hand-side. I really like how you explained it too, if it's okay if I use this when going over it with my friend. I used to be so good at this too haha. Thank...

I've been tutoring students at my college this semester, and came across this problem with a student: Show for all integers n\geqk\geq3, nCk - (n-3)C(k-3) = (n-1)Ck + (n-2)C(k-1) +(n-3)C(k-2) Since it's a combinatorial proof, I was looking at the number of ways that we could choose k...

PS: you're not old, you're awesome :) Heck, I couldn't figure it out, and MANY others I went to didn't even know where to start. I'm very happy that I was able to finally get it, and I think you should be too. :) You deserve a pat on the back!

lol I actually did something like that, and worked it out last night. I ended up getting 1/E^2 :) Combining and THEN taking the conjugate was what needed to be done. Thank you so much for your help! I feel very prepared for my final now :blushing:

If it does diverge, could I show that using the definition of a limit and reach a contradiction? I've been working on this for days, and the way the question is worded, it leads the student to think that the series converges. This is just a problem to help me prepare for the final, since it is...

I think it looks fine. :)

I squared everything and then simplified. I've come to realize however, that it's not something I shouldn't have done, but I wasn't thinking clearly at the time. I'm stuck when it comes down to the algebra: I know the limit is 0, so I just need to simplify my expression... I can then find a...

Well, I want to make sure that what I'm doing is correct. I've gone to my professor's office, and he wasn't very helpful to me. (there's a language barrier) Either way, does my N make sense and is mathematically correct? I wanted to get an N without squaring it as well, so I don't think...

But I don't have a square root in the numerator; it's just in the denominator. I'm slightly confused, but will keep looking at it - in case it was me. :( Here's what I did: I have that my above sequence is equal to \frac{3n^2}{n^2+3n+2} < \frac{3n^2}{n^2+3n} < E and my N = \frac{2E}{3-E}

Prove using the definition of a limit, Please help! :) Homework Statement Prove using only the definition of a limit, that the sequence: \frac{n}{(n+1)^1/2} - \frac{n}{(n+2)^1/2} converges. Homework Equations Let E>0 and choose a special N = something*E that whenever n>N our difference...

Yes it is - Thanks for jump starting my brain, haha :)

Homework Statement Find simple formulas for 1+ cos(θ) + cos(2θ) + cos(3θ) + ... + cos(nθ) and sin(θ) + sin(2θ) + sin(3θ) + ... + sin(nθ) The Attempt at a Solution It's not really a homework question, but more for making a problem that I'm trying to solve a little bit more simple...

Maybe try using the conjugate of the denominator and multiplying that by the top and bottom of your fraction. I think that could help, but I also think that there may be more information needed to solve this. :(

lol awesome! I just was thinking that it was the most reasonable way to tackle the problem. Thanks again! I'll post if I have any other questions :))

Homework Statement Prove that (1 + 1/n)^n = 1 + \sum1/m!(1 - 1/n)(1-2/n)...(1-(m-1)/n) where our sum is from m=1 to n. 2. Attempt: I recognize the binomial theorem here, but I'm having a mental block in how to figure this out. I should know how to do this, I think I just need a little help...