Induction Question (1 Viewer)

[cutemouse]

Hi could someone please do this question for me please? Thanks

Use mathematical induction to prove for all positive integers n that: xⁿ-1 is divisible by x-1

Thanks again.

 

[Timothy.Siu]

Hi could someone please do this question for me please? Thanks

Use mathematical induction to prove for all positive integers n that: xⁿ-1 is divisible by x-1

Thanks again.

i.e. xⁿ-1 = P(x-1)
test for n=1,

LHS=x-1 which is divisible by x-1
assume true n=k
x^k-1 = P(x-1)
prove for n=k+1
x^k+1-1 = Q(x-1)
LHS=x.x^k-1
=x(x^k-1)+x-1
=x(P(x-1)+x-1=(x-1)(Px+1) which is divisible by x-1