1) show that 9/ (n^3+(n+1)^3+(n+2)^3) ,n belongs N ,throhg
a) induction b)direct
57/(7^n+2 +8^2n+1) , n blongs N , throgh
a) induction b)congrunce
Here's the first one . . .
is a multiple of 9.1) Show that is a multiple of 9, for
a) by induction
Verify , which is a multiple of 9.
Assume , for some integer
Add to both sides:
We must show that the right side is a multiple of 9.
The right side is: .
The inductive proof is complete.
b) by direct proof.
We must show that either or is a multiple of 3.
There are three cases for
. . .Then: . , a multiple of 3.
. . .
. . .