Thanks :) III. Are the following statements true or false? If the statement is false, justify your answer.1. Let {a„} and {bn} be sequences such that an < b, for all n, lim a,lim bn = b. Then a > b.а, аndn-002. Suppose {a,} and {bn} are sequences with_lim a, = a and lim (a, – bn) = 0. Then,lim b, = a.n-00n +13. The infinite seriesis divergent. Then for any constant c, the series(n +2n+1is also divergent.n+24. An infinite series of the form (an – bn) is always divergent given that bothanand bn are divergent.n=1

Name: Thanks :) III. Are the following statements true or false? If the stat
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Description: Thanks :) III. Are the following statements true or false? If the statement is false, justify your answer.1. Let {a„} and {bn} be sequences such that an b.а, аndn-002. Suppose {a,} and {bn} are sequences wit

To check if the following statements are true or false. If false, we have to justify. (1) Let {an}…

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III. Are the following statements true or false? If the statement is false, justify your answer. 1. Let {a„} and {b,} be sequences such that a, < b, for all n, lim a, = a, and lim bn = b. Then a > b. 2. Suppose {a,} and {bn} are sequences with lim an = a and lim (an – bn) = 0. Then, lim b, = a. n + 1 is divergent. Then for any constant e, the series n+ 2 3. The infinite series n+1 n+2 is also divergent. 4. An infinite series of the form (an – bn) is always divergent given that both an and bn are divergent.

III. Are the following statements true or false? If the statement is false, justify your answer. 1. Let {a„} and {b,} be sequences such that a, < b, for all n, lim a, = a, and lim bn = b. Then a > b. 2. Suppose {a,} and {bn} are sequences with lim an = a and lim (an – bn) = 0. Then, lim b, = a. n + 1 is divergent. Then for any constant e, the series n+ 2 3. The infinite series n+1 n+2 is also divergent. 4. An infinite series of the form (an – bn) is always divergent given that both an and bn are divergent.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Thanks :)

III. Are the following statements true or false? If the statement is false, justify your answer.
1. Let {a„} and {bn} be sequences such that an < b, for all n, lim a,
lim bn = b. Then a > b.
а, аnd
n-00
2. Suppose {a,} and {bn} are sequences with_lim a, = a and lim (a, – bn) = 0. Then,
lim b, = a.
n-00
n +1
3. The infinite series
is divergent. Then for any constant c, the series
(n +2
n+1
is also divergent.
n+2
4. An infinite series of the form (an – bn) is always divergent given that both
an
and bn are divergent.
n=1

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