1) show that 9/ (n^3+(n+1)^3+(n+2)^3) ,n belongs N ,throhg

a) induction b)direct

2)show that

57/(7^n+2 +8^2n+1) , n blongs N , throgh

a) induction b)congrunce

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- Nov 22nd 2008, 04:12 AMhogersolve that
1) show that 9/ (n^3+(n+1)^3+(n+2)^3) ,n belongs N ,throhg

a) induction b)direct

2)show that

57/(7^n+2 +8^2n+1) , n blongs N , throgh

a) induction b)congrunce - Nov 22nd 2008, 10:29 AMSoroban
Hello, hoger!

Here's the first one . . .

Quote:

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.

Quote:

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.

. . .

. . .

. .