Let {xn} denote a sequence of real numbers i. Define what it means for the sequence {xn} to converge, using the usual E and N notation. ii. Define what it means for the sequence {xn} to be strictly increasing. iii. If the sequence is bounded above then define the least upper bound (i.e. the supremum) of {xn} . iv. If a sequence {xn} is both increasing and bounded above then state what you can deduce about the convergence or divergence of the sequence?
Let {xn} denote a sequence of real numbers i. Define what it means for the sequence {xn} to converge, using the usual E and N notation. ii. Define what it means for the sequence {xn} to be strictly increasing. iii. If the sequence is bounded above then define the least upper bound (i.e. the supremum) of {xn} . iv. If a sequence {xn} is both increasing and bounded above then state what you can deduce about the convergence or divergence of the sequence?
Chapter9: Sequences, Probability And Counting Theory
Section9.1: Sequences And Their Notations
Problem 63SE: Follow these steps to evaluate a finite sequence defined by an explicit formula. Using a Tl-84, do...
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Let {xn} denote a sequence of real numbers i. Define what it means for the sequence {xn} to converge, using the usual E and N notation.
ii. Define what it means for the sequence {xn} to be strictly increasing.
iii. If the sequence is bounded above then define the least upper bound (i.e. the supremum) of {xn} .
iv. If a sequence {xn} is both increasing and bounded above then state what you can deduce about the convergence or divergence of the sequence?
(d) Explain why each of the following sequences converges and in the case of i. and ii. determine the limits.
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