binomial help please! (1 Viewer)

[desperate cat]

can some one show me how to do this? thanx

use the binomial theorem to show that 7^n + 2 is divisible by 3, where n is a positive integer. (hint: write 7 = 6+1)

 

[Templar]

7^n+2=(6+1)^n+2
=6^n+nC1*6^(n-1)+nC2*6^(n-2)+...+nC(n-1)*6+1+2
=6^n...nC(n-1)*6+3

Take out common factor of 3.

 

[desperate cat]

oic, thanks heaps