What is the formula for solving of induction?

Answer 1

Induction is not a formula, it is a method of proof.

Anyway, state the property you wish to prove about each natural number n. This is usually the given P(n).

Prove this for the zeroth case, i.e. P(0).

Assume the nth case is true, i.e. P(n). Show P(n) => P(n+1).

Example:

Prove 2 + 4 + ... + 2n = n(n+1) for n >= 0

Proof: P(0) = 0 trivially.

Assume: P(n)

Show P(n) => P(n+1).

1. 2 + 4 + ... + 2n = n(n+1)

2. 2 + 4 + ... + 2n + 2(n+1) = n(n+1) + 2(n+1) = (n+1)(n+2). QED