必威体育精装版微积分(下)英文教材 .pdf

Chapter 1 Infinite Series Generally, for the given sequence a1 , a 2 , a3 an ,, the expression a a a a formed by the sequence 1 , 2 , 3 n ,, a1 a 2 a 3 an , is called the infinite series of the constants term, denoted by a n , that n 1 is a n =a1 a2 a3 a n , n 1 Where the nth term is said to be the general term of the series, moreover, the nth partial sum of the series is given by Sn a1 a 2 a3 an . Determine whether the infinite series converges or diverges. Whil e it ’s possible to add two numbers, three numbers, a hundred numbers, or even a million numbers, it ’impossibles to add an infinite number of numbers. To form an infinite series we begin with an infinite sequence of real numbers: a , a ,a ,a , we can not form the sum of all the a (there is 0 1 2 3 k an infinite number of the term), but we can form the partial sums 0 S0 a0 ak k 0 1 S1 a0 a1 a k k 0 2 S2 a0 a1 a2 a k k 0 3 S3 a0 a1 a2 a3 a k k 0 ………………. n Sn