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