Question

Use a proof by induction to show that, −(16−11?) is a positive number that is divisible...

  1. Use a proof by induction to show that, −(16−11?) is a positive number that is divisible by 5 when ? ≥ 2.

  2. Prove (using a formal proof technique) that any sequence that begins with the first four integers 12, 6, 4, is neither arithmetic nor geometric.

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Answer #1

First we will prove by induction that is a positive number for .

For n= 2 ,

, which is positive .

Suppose the statement is true for n= m that is . Then for n=m+1 ,

So ,

That is the statement is true for n=m+1 . Hence is positive for .

But the statement is divisive by 5 for is not an true example .

For n=2 ,

, which is not divisible by 5 .

.

.

If you have doubt at any step please comment.

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