tailieunhanh - CHAPTER 5 INFINITE SEQUENCES AND SERIES - SERIES

We can add the terms of a sequence {an } and get an expression of the form: a1+ a2+ a3+ + an + which is called a series and denoted by However what does it mean by the sum of infinitely many terms? Example. We can try to add the terms of the series 1+2+3+ +n+ and get the cumulative sums 1, 3, 6, 10, , The nth sum n(n+1)/2 becomes very large as n increases | CHAPTER 5 INFINITE SEQUENCES AND SERIES CONTENTS . Sequences . Series . The Integral and Comparison Test . Other Convergence Test . Power Series . Representations of Functions as Power Series . Taylor and Maclaurin Series . The Binomial Series . Applications of Taylor Polynomial . Using Series to solve Differential Equations . Fourier Series . SERIES . The Sum of a Series . Geometric Series . The Test for Divergence . Properties of Convergent .

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