Recent content by ruud

Nevermind I just heard from a fellow friend that this statement is false.

I'm stuck and not sure what I've done wrong for this problem Prove the following by mathematical induction: 1^3 + 2^3 + 3^3 + 4^3 ... + n^3 = ((n^2 + n)/2)^3 ok so I proved it for n = 1 and n = 2 then assume n = k so ((k^2 + k)/2)^3 Then let's try to do n = k +1 so ((k+1)^2 + k...

Could you please explain further

I'm having trouble with two parallelogram proofs 1) PQRS is a parallelogram and T is any point inside the parallelogram. Prove that triangle TSR + triangle TQP = 1/2 parallelogram PQRS 2) ABCD is a quadrilateral whose area is bisected by the diagonal AC. Prove that BD is bisected by AC...

I forgot to mention F is the point where the two medians cross

I can't figure out this problem Lets take triangle ABC A B C a median (D) goes from A to the midpoint of BC a median (E) goes from B to the midpoint of AC Prove that triangle AEF = triangle FBD Since a median divides up a triangle you know that triangle ABD = triangle...

1. 2003 2. 5

I'm getting confused and can't seem to wrap my head around this problem. Prove that the sum of the squares of any 3 consecutive odd numbers when divided by 12 gives a remainder of 11. I'm not sure how to set this up or proceed I figured that (n^2 + (n +2)^2 + (n+4)^2)/12 = x + 11...

I think I got it now thanks for your help

here is a question that I need help with 1) In triangle KLM, P is the midpoint of the line segment LM. Prove that if PL = PK =PM, angle LKM = 90 L |\ | \P | \ |__ \ K M If someone could set up the problem I'd be greatful

I wouldn't say safely could you please expand on that? every time a number that ends with 5 is squared the resulting term ends in 25

any positive number that ends in 5 when squared ends in 25 eg 5^2 = 25 15^2 = 225 25^2 = 625 Just scrap what I started with I don't think it helps at all, how could I prove this question?

This should be an easy question but I'm having problems with it. Prove that any number that ends in five when squared equals 25. So if n is the number then (n/5)^2 = (n^2)/25 Although if you expand the left side then this statement is redudant. Can someone help me with this?

The problem is that x/0 doesn't equal anything it is undefined.