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MATHEMATICS Convergent sequence
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Exercise 26: Calculate the limit
.Solution: Please, note that
, so we have the following limit
.
In the numerator we exclude such a word before the bracket, after which the exemption in the numerator will be the limits other then +K and - K. We exclude from bracket 3n*n2.
In the denominator we exclude such a word before the bracket, after which the exemption in the denominator will be the limits other then +K and - K, and in order to the limit of denominator was distinct to 0. We exclude from bracket 3n*n2. We have
The sequences
are convergent
to 0, the numerators are convergent to 1, and the denominators are diverge ( -K
). The sequence
is geometric
sequence with
quotient
.
Therefore