Question

Estudier, here's my question.

Answer 1

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

Answer 2

Pythagorus?

Answer 3

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

Answer 4

Yup, I got that...:-)

Answer 5

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.

Answer 6

I suppose just use the formula for a proof, lol

Answer 7

lolol, i guess.

Answer 8

T_n-1 + Tn = n^2

Answer 9

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

Answer 10

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

Answer 11

Do u have to prove T_n?

Answer 12

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.

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

I suspect it will get harder quite quickly..

Answer 19

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 >.>

Answer 20

Just to practice induction, I guess...:-)

They use a lot in number theory.

Answer 21

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

Answer 22

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

Answer 23

oo, that sounds interesting lol

Answer 24

Oops, I made it wrong..wait.

Answer 25

kth n-gon number?

Answer 26

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

Answer 27

or that lolol

Answer 28

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

Answer 29

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