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carlalopezelox2244
07.03.2020 •
Mathematics
Let{an}[infinity]n=1be a sequence. A real numberxis alimit point(sometimes called anaccumulation point) if there is a subsequence{ank}[infinity]k=1which converges tox.(a) How many limit points do the following sequences have?(i){(−1)n}[infinity]n=1(ii)an= 10 ifn= 1, . . . ,100 andan=1nifn >100.(b) Construct a sequence that does not have a limit point.(c) Construct a sequence with exactly 2 limit points.(d) Construct a sequence that has exactly one limit point, but which does not con-verge.
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Ответ:
Answer for the question is explained din the attachment.
Step-by-step explanation:
a. i. Sequence has only two limit point
ii. Sequence is convergent and have only one limit point.
b. We have maked sequence that not have a limit point.
c. We have maked sequence that has two limit point.
d. We constructed a sequence that has only one limit point but not convergent.
Ответ:
0.89898989.... is the correct answer
Fraction form:![\frac{89}{99}](/tpl/images/2648/6841/a99ac.png)
Step-by-step explanation:
0.89898989.... is the correct answer because it can be written as
in the simplest form. and 0.89898989.... is rational because it is a repeating number.
Any rational number is a number that can be written as a fraction, a repeating decimal, a whole number, an integer, etc. As long as the number is a number with infinite digits like π.