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MATHEMATICS Convergent sequence
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Exercise 2: Calculate the limit
.Solution: We divide the numerator and the denominator by the highest power of variable n appearing in the denominator. We divide the numerator and the denominator by n3
.
Please note that all the sequences
appearing in the numerator and
denominator are finite limits. Then in accordance with
theorm of If
is a real number, then
We have
Thus we can apply the theorem: If a sequence
has limit a, and a sequence
has limit b ( where
), then
and
,
for
,
thus