REAL ANALYSIS LECTURE #2 | CHARLES G. DENLINGER | EXERCISE PROBLEMS 8.1 AND 8.2

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 ...