Estudier, here's my question.

i want to just point to the picture and say, "you did the work for me"

Pythagorus?

oh, it doesnt say it in the problem, but t_n are the triangular numbers, where: \[t_n = \sum_{i=1}^{n}\space i\]

Yup, I got that...:-)

i just dont see what to write formally as an answer. I mean, the problem tells you how to solve it <.< all the work is there.

I suppose just use the formula for a proof, lol

lolol, i guess.

T_n-1 + Tn = n^2

maybe i can use that. had to prove that for an earlier problem.

2 triangular numbers make a square number.....

Do u have to prove T_n?

right right. i dont think ive run into a problem that tells you how to solve it lol <.< I didnt have to prove what t_n was, that was done in the section as an example.

This question (im guessing) wants you to prove the formula for t_n in a different manner, by making that array of dots.

it just seems too......trivial though. i hate using that word =/ but it really is.

So T_n-1 + T_n = 1/2(n-1)n + 1/2(n+1)n = n^2

i have class tomorrow, homework isnt due till monday. I'll voice my concerns to the professor.

There isn't much to do but this is typical number theory intro stuff, get u into proof mode....

I suspect it will get harder quite quickly..

There was another problem i was having trouble doing too. Prove that:\[(x-y)|x^n-y^n\] by Mathematical Induction. Now, using the geometric formula its easy because: \[x^n-y^n = (x-y)(x^{n-1}+x^{n-2}y+\ldots+y^{n-1})\]so x-y always divides x^n-y^n. But how (or WHY?!?!) would you do it by induction? o.O its like making a mountain out of a mole hill >.>

Just to practice induction, I guess...:-) They use a lot in number theory.

*sigh* i guess. well, im gonna get back to work on this then. i'll ask about it during class as well lol. thanks :)

Here is a harder one, get a formula for the k'th polygonal number.

oo, that sounds interesting lol

Oops, I made it wrong..wait.

kth n-gon number?

Get P(k,n) the nth k-gonal number.

or that lolol

I knew what I wanted to say and mouth got into gear before brain....

i understood it as well lol. im gonna think about that. need to finish the homeworks first though.

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