REAL ANALYSIS LECTURE #2 | CHARLES G. DENLINGER | EXERCISE PROBLEMS 8.1 AND 8.2
Автор: COSMOS LEARNING
Загружено: 2023-02-28
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IN THIS VIDEO FORM THE EXERCISE PROBLEMS OF 8.1 AND 8.2 OF THE BOOK ELEMENTS OF REAL ANALYSIS BY CHARLES G. DENLINGER ARE DISCUSSED!
1. Prove Theorem 8.2.2.
2. Prove Theorem 8.2.6. Also, express this theorem using the language of
one series "dominating" another.
In Exercises 3- 12, write the given series in the form I: an and use tests
given in Sections 8.1 and 8.2 to determine whether the series converges
or diverges.
5. Prove that altering or deleting a finite number of terms of an infinite
series does not affect its convergence or divergence.
6. Prove that every sequence {an} is the sequence of partial sums of some
series L Xk·
about the infinite, nonterminating decimal 0.99999999 · · · ?
2. Find the sum of each of the following series, if it converges:
(a) 0.0101010101 · · · (b) 0. 987698769876 ...
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