- #1
jonroberts74
- 189
- 0
prove (induction) [tex]6|7^{n}-1; \forall n \ge 0[/tex]
P(0)
[tex]6|7^0 -1[/tex]
6|0
P(k)
[tex]6|7^k-1[/tex]
what I want to show: [tex]6|7^{k+1}-1[/tex]
I know I'll kick myself but this one isn't jumping out at me.
[tex]7 \cdot 7^k-1[/tex]
maybe something with [tex](6+1)^k(6+1)-1[/tex]
P(0)
[tex]6|7^0 -1[/tex]
6|0
P(k)
[tex]6|7^k-1[/tex]
what I want to show: [tex]6|7^{k+1}-1[/tex]
I know I'll kick myself but this one isn't jumping out at me.
[tex]7 \cdot 7^k-1[/tex]
maybe something with [tex](6+1)^k(6+1)-1[/tex]