Recent content by nyr91188

I did (26)8 + (8 choose 2)*(26)7 + (8 choose 3)*(26)6 + (8 choose 4)*(26)5 + (8 choose 5)*(26)4 + (8 choose 6)*(26)3 + (8 choose 7)*(26)2 + 26 This is based on no repetition + exactly 1 rep. + exactly 2 rep. + exactly 3 rep. + exactly 4 rep. + exactly 5 rep. + exactly 6 rep. + exactly 7 rep...

Sorry, I'm not really stuck. I just can't ever be sure that I'm even on the right track with these kind of problems. So, I just wanted to get some input to make sure I'm not way off. Thanks for your help.

That's the exact question from the book. It means either no letters are repeated or one letter can be repeated as many times as you want. I didn't learn inclusion/exclusion yet so I don't think we are supposed to use it. So, I counted the ways in which there is no repetition, there is...

Homework Statement How many eight-letter passwords using the letters A-Z are there in which up to one letter is allowed to be used more than once? Homework Equations The Attempt at a Solution I broke the problem up based on repetition of one letter: (26)8 ways with no...

Also, I don't understand what would be wrong with proving lim(xn-yn)=lim(xn)-lim(yn) [which I now figured out how to prove correctly], and then say that assuming xn→x then 0=x-lim(yn) and lim(yn)=x. Otherwise, if xn does not approach x, then of course yn is also divergent.

I meant you as a general you, meaning whoever is doing the proof, meaning me. Anyway, I'm not looking for answers so calm down. I'm just trying to understand the steps of the proof. Does limn→∞(xn-yn)=0 mean that xn and yn converge to the same value (namely, that x=y)?

But you still have to prove that if both of them converge that they converge to the same value? I don't quite understand what is implied by limn→∞|xn-yn|=0. Does this mean the lim(xn)→lim(yn)?

(2) is basically correct except that it should be tan^2 since the derivative of tan^3 is 3tan^2...

Homework Statement Suppose {Xn}, {Yn} are sequences in ℝ and that |Xn-Yn|→0. Show that either: a) {Xn} and {Yn} are both divergent or b) {Xn} and {Yn} have the same limit. Homework Equations N/A The Attempt at a Solution I first prove that lim(Xn-Yn)=lim(Xn)-lim(Yn). I am not...