University:
University of Central Florida
Course:
MAC 2312 | Calculus with Analytic Geometry II
Academic year:

2023
Views:

446

Pages:

5
Author:

Maria

Infinite Series 5.2. SERIES Ean = a + ₂ + az + ay +.... 1+1 2 + +1 - 2 4 16 Sequence of partial sums [Sn for a series & an If lim Sn ONE then an diverges 1-300 Sza, taz Sza, ta taz Sya, ta + azt au Σ an Lim Sn if it exists. If lim In exists then & an converges n-300 7-1 geometric series. common ratio Ex: 5(2 n-1 5 + 10 + 20+ 40+ 80 +.... Sn = a + ar + ar² + .... + ar?! 7-1 Sn = ar + ar²t an't 2 + ar + arn Sn-rsn=a-ar" Sn (1-r)=a-ar" 4-1 Sna 1- 2 ar = lim a 1- 1-r When does lim a 1-1 converge? J-1 npo lim alr = lim lim I lim J-1 A-) Do a 7-150 4-300 Um I - lim 3308 n When does lim " converge? if r1 = 0∞ diverge n if (1) diverge (-) = (-1)^" with cl if = 1 lim1 = 1 => diverge if r=-1 lim 1:1 diverge - converges Sum is 5 1--2 5 3 5. 3 S = 3 8 "converge? We need & ar Ex: Does 23" converge? 1-8 = 243 = 4.43" n=1 22=(22)-4 n-1 Geometric series = =) diverges 11=1>1) diverges