Induction Help (1 Viewer)

[205021]

Hi, i need help with a question about induction plocks:

Prove the following by induction where n is a positive integer:

x^n - 1 is divisible by x-1

and (sepereate question)

n(n+1)(n+2) is divisible by 3

cheers.

 

[shaon0]

Hi, i need help with a question about induction plocks:

Prove the following by induction where n is a positive integer:

x^n - 1 is divisible by x-1

and (sepereate question)

n(n+1)(n+2) is divisible by 3

cheers.

Let n=k:
Assume, x^k-1=M(x-1) where M,x E Z

Let n=k+1:
x^(k+1)-1=x^k.x-1
=xM(x-1)+x-1 from assumption
=(x-1)[Mx+1]
=N(x-1) where N E Z: N=Mx+1

Let n=k:
Assume, k(k+1)(k+2)=3M where M E Z

Let n=k+1:
LHS=[(k+1)(k+2)](k+3)
=k(k+1)(k+2)+3(k+1)(k+2)
=3M+3(k+1)(k+2)
=3N where N=M+(k+1)(k+2)

 

[205021]

THANKS!

that helped alot. well done!

 

[shaon0]

THANKS!

that helped alot. well done!

Yeah, nw