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In this task, you will write a proof to analyze the limit of a sequence. ASSUMPTIONS...

In this task, you will write a proof to analyze the limit of a sequence.

ASSUMPTIONS

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

Let P be 6. and Let Q be 24.

Define your sequence to be an = 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.

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

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