# Questions involving Pascal's Triangle

• March 28th 2009, 07:32 AM
Rosella
Questions involving Pascal's Triangle
sorry for the other posts
here is the quest , i want u all to help me :

1.Factorize the expressions p(n)= n2 –n for Îí 2,3,4,5,ý.Determine if the expression is always divisible by the corresponding x. if divisible use mathematical induction to prove ur results by showing whether P( k+1) – P (k) is always divisible by x. using appropriate technology ,explore more cases, summarize ur results and make a conjecture for when nx-n is divisible by x.

2. Explain how to obtain the entries in Pascal’s triangle. And using appropriate technology, generate the first 15 rows. State the relationship between the expressions
P (k+1) – P (k) and the Pascal’s triangle. Reconsider Ur conjecture and revise if necessary.

Write an expression for the xth row of Pascal’s triangle, you will have noticed that
(xr) =k, k ÎN. Determine when k is a multiple of x.

3. Make conclusions regarding the last result in part 2 and the form of proof by induction used in this assignment. Refine ur conjecture if necessary, and prove it.

4. State the converse of ur conjecture. Describe how u would prove whether or not the converse holds.

thx a lot in advance for ur helps
• March 28th 2009, 08:53 AM
Jhevon
Quote:

Originally Posted by Rosella
sorry for the other posts
here is the question , i want you all to help me :

1.Factorize the expressions p(n)= n2 –n for Îí 2,3,4,5,ý.Determine if the expression is always divisible by the corresponding x. if divisible use mathematical induction to prove your results by showing whether P( k+1) – P (k) is always divisible by x. using appropriate technology, explore more cases, summarize your results and make a conjecture for when nx-n is divisible by x.

2. Explain how to obtain the entries in Pascal’s triangle. And using appropriate technology, generate the first 15 rows. State the relationship between the expressions
P (k+1) – P (k) and the Pascal’s triangle. Reconsider your conjecture and revise if necessary.

Write an expression for the xth row of Pascal’s triangle, you will have noticed that
(xr) =k, k ÎN. Determine when k is a multiple of x.

3. Make conclusions regarding the last result in part 2 and the form of proof by induction used in this assignment. Refine your conjecture if necessary, and prove it.

4. State the converse of your conjecture. Describe how u would prove whether or not the converse holds.

thanks a lot in advance for your help

First, please fix the formatting. there are some weird symbols in your post. Also, refrain from using chat speak. because this reeks of "graded assignment" i will not give you solutions, but guidelines.

for (1) note that $n^2 - n = n(n - 1)$

for (2) see here. there is an animation on the right that is nice. you may also want to see here

for (3) do you know what "proof by induction" means? answer the first two questions and tell me what you come up with as your conjecture for this one.

for (4), you need to do (3), so try to get to it quickly :)
• April 6th 2009, 06:29 AM
Rosella
hiii
thx u jhvon 4 ur help
i did it but for no2: , i'm geeting problem
And using appropriate technology, generate the first 15 rows. ( pascal'e traingle )
can someone help me plss
Thx a lot