Quick Binomial Q (1 Viewer)

[iSplicer]

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)

thanks guys =)

 

[addikaye03]

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)

thanks guys =)

(1+x)^n=nC0+nC1x+nC2x^2+nC3x^3+...+nCnx^n

Add +2, Let x=6

 

[iSplicer]

Cheers mate, sorry, I'm just starting this topic, completely missed that seemingly obvious step

Thanks again

 

[Drongoski]

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)

thanks guys =)

Couldn't get LaTeX to work.

Basically 7ⁿ + 2 = (1+6)ⁿ + 2

= sigma {r = 0 t0 n} nCr 6^r + 2

= sigma{r = 1 to n} nCr 6^r + 1 + 2

= sigma {r=1 to n} nCr 6^r + 3

= all terms now multiples of 3

= divisible by 3

 

[iSplicer]

Couldn't get LaTeX to work.

Basically 7ⁿ + 2 = (1+6)ⁿ + 2

= sigma {r = 0 t0 n} nCr 6^r + 2

= sigma{r = 1 to n} nCr 6^r + 1 + 2

= sigma {r=1 to n} nCr 6^r + 3

= all terms now multiples of 3

= divisible by 3

Sweet, thanks =)