# 8.1 Notes - Limit of a Sequence Let L be a real number Let...

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Calculus II Section 8.1 – Sequences A sequence is a function whose domain is the set of natural numbers. Write the first 5 terms of the sequence 1 n a n Compare: 1 ) ( x x f and 1 n a n Write the first 5 terms of the sequence )! 1 ( ! 3 n n a n Simplify: ! )! 2 ( n n Simplify: )! 2 ( )! 2 2 ( n n

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We also need to be able to write the formula for the nth term of a sequence if we are given a few of the terms. Note that we are really finding the apparent formula because we can’t really be sure what comes next we can only go by the pattern that appears to be happening. Write an expression for the nth term of the following sequences:
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Unformatted text preview: Limit of a Sequence Let L be a real number. Let f be a function of a real variable such that L x f x ) ( lim . If n a is a sequence such that n a n f ) ( for every positive integer n , then L a n n lim . Evaluate: n n e n sin lim = n n n n n 4 2 1 3 lim 3 2 = Determine the convergence or divergence of the sequence where n n a ) 1 ( 1 . Determine the convergence or divergence of the sequence where n n a n 1 sin . Determine the convergence or divergence of the sequence where n n n a 1 2 ....
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8.1 Notes - Limit of a Sequence Let L be a real number Let...

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