Assumption:

Definition: A sequence {a_n} for n = 1 to converges to a real number A if and only if for each > 0 there is a positive integer N such that for all n N, |a_n - A| < .

Let P be a whole number that corresponds to the month of your birth (e.g., February corresponds to 2, March corresponds to 3). If you were born in January, use 13 as your value for P.

Let Q be a whole number that corresponds to the day of the month you were born.

Note: For example, if you were born on May 24, the value forPwould be 5 and the value forQwould be 24.

Define your sequence to be a_n = 4 +

1

Pn + Q

, where n is any positive integer.

A. Compute a positive integer N that is appropriate to prove your sequence converges to a limit of 4. Show your work.

1. Using the formal definition provided in the Assumptions section, prove, for > 0, that a_n converges to a limit of 4. Justify your work.