A CLASS ASSIGNED PROBLEM FOR PHYSICS 555ASPRING 2008. CSUF

BY NASSER ABBASI

Show that the recurence formula

| (1) |

can be written as

| (2) |

Proof by induction on . For , equation (1) becomes

and equation (2) becomes

Hence it is true for . Now assume it is true for , in otherwords, assume that

| (3) |

implies

| (4) |

Now for the induction step. we need to show that it is true for , i.e. given (4) is true, we need to show that, by replacing by in the above, that

| (5) |

implies

We start with (5), and replace the term with what we assumed to be true from (4), hence (5) can be rewritten as

Simplify the above leads to

Which is (6). Therefore, the relationship is true for any . QED