State if the sequence {xn}1 define below is convergent or divergent: fix -1< a < 1, and let xn = n·a" for n = 1,2, ....

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 81E
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1. Write the final answer of the following questions; no justification is required.
T/F mean true or false; FIB means fill the best mathematical choice in the blanks.
(a) State if the sequence {xn}1 define below is convergent or divergent: fix -1 <
a < 1, and let xn = n· a" for n = 1,2, ....
(b) State if the sequence {xn} define below is convergent or divergent: fix b > 0,
and let xn = b" /n! for n = 1, 2, . . .
(c) Let E-1 xk be a convergent series of real numbers. Then 1 *k, is convergent
for
any subsequence {k;}1 of {1,2,3, ...}.
(d) (T/F) Let{xn}=1 and {Yn}n=1 are convergent sequences.
{vn}1 defined by vn = min{x, Yn} is also convergent.
Then the sequence
Transcribed Image Text:1. Write the final answer of the following questions; no justification is required. T/F mean true or false; FIB means fill the best mathematical choice in the blanks. (a) State if the sequence {xn}1 define below is convergent or divergent: fix -1 < a < 1, and let xn = n· a" for n = 1,2, .... (b) State if the sequence {xn} define below is convergent or divergent: fix b > 0, and let xn = b" /n! for n = 1, 2, . . . (c) Let E-1 xk be a convergent series of real numbers. Then 1 *k, is convergent for any subsequence {k;}1 of {1,2,3, ...}. (d) (T/F) Let{xn}=1 and {Yn}n=1 are convergent sequences. {vn}1 defined by vn = min{x, Yn} is also convergent. Then the sequence
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