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- Jul 4th 2007, 10:52 PMRaiden_11polygons and triangles
- Jul 4th 2007, 11:41 PMred_dog
Question 1:

- Jul 4th 2007, 11:45 PMred_dog
Question 2:

- Jul 4th 2007, 11:50 PMred_dog
Question 3:

If then

In this case - Jul 4th 2007, 11:57 PMred_dog
Question 4:

is exterior to triangle . So (1).

is exterior to triangle . So (2).

From (1) and (2) via tranzitivity, yields - Jul 5th 2007, 05:10 AMearboth
Hello,

to question 2:

I've modified your drawing (see attachment):

The angle in red is an exterior angle of the isosceles triangle ACD;

the angle in blue is an exterior angle of the isosceles triangle ABD.

The angle at the centre is 2x + 2y = 2(x+y) that means it is twice as large as the angle at C. - Jul 5th 2007, 06:21 AMSoroban
Hello, Raiden_11!

Basically the same as red_dog . . .

Quote:

. .

In

Therefore: .

- Jul 5th 2007, 10:02 AMRaiden_11Can u help me with these?
2. Observe the relationship between the elements of Diagonal 1 and Diagonal 2 in Pascal’s Triangle, shown on the next page. The sum of the first two elements in Diagonal 1 is equal to the second element in Diagonal 2. Similarly, the sum of the first 5 elements of Diagonal 1 is equal to the 5th element of Diagonal 2. Suppose we wish to use Pascal’s Triangle to find the sum of the first

*n*natural numbers. Use combinatorial notation to express the sum of the*n*elements of Diagonal 1 in terms of the corresponding value in Diagonal 2.

http://www.mathhelpforum.com/math-he...ase-pascal.jpg

**3.**Using the method of mathematical induction, prove that the following statements are false.

http://www.mathhelpforum.com/math-he...ease-sigma.jpg - Jul 5th 2007, 10:22 AMred_dog
2.

3.

For the first identity:

For

For

For , false. So the identity is not true for all .

For the second identity:

For , false. So the identity is not true for all . - Jul 5th 2007, 11:27 AMRaiden_11Last thing i'll ever need from you!?