Calculus BCL105 - Sequences

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Calculus BC L105 - Sequences
Sequences
Ex1. Write the first four terms in the sequence
if n 1, 2, 3,
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Ex2. Write the generator form for the following
sequence for n 1,2,3,
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LIMIT OF A SEQUENCE
A sequence an converges to L or has a limit L
written
If for any e gt 0 there exists and integer N such
that
for all n N.
If the sequence an does not converge, then we
say it diverges.
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Ex3. Determine whether each sequence converges
or diverges.
converges to 1
converges to e
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LIMIT RULES FOR SEQUENCES
If an and bn are convergent sequences and if
and
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DEFINITION OF INCREASING, DECREASING AND MONOTONIC
A sequence an is said to be increasing if an1
an for all n gt 1.
A sequence an is said to be decreasing if an1
an for all n gt 1.
A sequence is said to be monotonic if it is
either increasing or decreasing.
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DEFINITION OF BOUNDED
A sequence an is said to be bounded above if
there is some number M such that
A sequence an is said to be bounded below if
there is some number m such that
A sequence that is both bounded above and bounded
below is simply said to be bounded.