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,ư.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