Series Ch. 13. A series is an indicated sum of the terms of a sequence. Finite sequence: 2, 4, 6, 8...
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Transcript of Series Ch. 13. A series is an indicated sum of the terms of a sequence. Finite sequence: 2, 4, 6, 8...
![Page 1: Series Ch. 13. A series is an indicated sum of the terms of a sequence. Finite sequence: 2, 4, 6, 8 Finite series: 2+ 4 + 6 + 8 = 20 Infinite sequence:](https://reader036.fdocuments.us/reader036/viewer/2022072016/56649ef65503460f94c0a62b/html5/thumbnails/1.jpg)
SeriesCh. 13
![Page 2: Series Ch. 13. A series is an indicated sum of the terms of a sequence. Finite sequence: 2, 4, 6, 8 Finite series: 2+ 4 + 6 + 8 = 20 Infinite sequence:](https://reader036.fdocuments.us/reader036/viewer/2022072016/56649ef65503460f94c0a62b/html5/thumbnails/2.jpg)
A series is an indicated sum of the terms of a sequence.
Finite sequence: 2, 4, 6, 8Finite series: 2+ 4 + 6 + 8 = 20
Infinite sequence: 2, 4, 6, 8, 10, …..Infinite series: 2 + 4 + 6 + 8 + 10 + …
Series
![Page 3: Series Ch. 13. A series is an indicated sum of the terms of a sequence. Finite sequence: 2, 4, 6, 8 Finite series: 2+ 4 + 6 + 8 = 20 Infinite sequence:](https://reader036.fdocuments.us/reader036/viewer/2022072016/56649ef65503460f94c0a62b/html5/thumbnails/3.jpg)
Sn indicates the sum of the first n terms of the series.
S12 means to add up the first 12 terms of the series.
S100 means to add up the first 100 terms of the series.
Sn
![Page 4: Series Ch. 13. A series is an indicated sum of the terms of a sequence. Finite sequence: 2, 4, 6, 8 Finite series: 2+ 4 + 6 + 8 = 20 Infinite sequence:](https://reader036.fdocuments.us/reader036/viewer/2022072016/56649ef65503460f94c0a62b/html5/thumbnails/4.jpg)
Find the sum of the first 50 terms of the arithmetic series 11 + 14 + 17 + 20+ ….
Sum of a Finite Arithmetic Series
1( )
2n
n
n t tS
![Page 5: Series Ch. 13. A series is an indicated sum of the terms of a sequence. Finite sequence: 2, 4, 6, 8 Finite series: 2+ 4 + 6 + 8 = 20 Infinite sequence:](https://reader036.fdocuments.us/reader036/viewer/2022072016/56649ef65503460f94c0a62b/html5/thumbnails/5.jpg)
Find the sum of the first ten terms of2 – 6 + 18 – 54 + …..
Sum of a Finite Geometric Series
1(1 )
1
n
n
t rS
r
![Page 6: Series Ch. 13. A series is an indicated sum of the terms of a sequence. Finite sequence: 2, 4, 6, 8 Finite series: 2+ 4 + 6 + 8 = 20 Infinite sequence:](https://reader036.fdocuments.us/reader036/viewer/2022072016/56649ef65503460f94c0a62b/html5/thumbnails/6.jpg)
1. Find S10 of the arithmetic series if:
t1 = 3 and t10 = -206.
2. S20 if 5 + 10 + 15 + 20 + …….
Problems
![Page 7: Series Ch. 13. A series is an indicated sum of the terms of a sequence. Finite sequence: 2, 4, 6, 8 Finite series: 2+ 4 + 6 + 8 = 20 Infinite sequence:](https://reader036.fdocuments.us/reader036/viewer/2022072016/56649ef65503460f94c0a62b/html5/thumbnails/7.jpg)
1. Find S10 if 1 + .5 + .25 + .125 + …..
2. Find Sn if, a1 = -3, an = -786432, r = 4
Problems #2
![Page 8: Series Ch. 13. A series is an indicated sum of the terms of a sequence. Finite sequence: 2, 4, 6, 8 Finite series: 2+ 4 + 6 + 8 = 20 Infinite sequence:](https://reader036.fdocuments.us/reader036/viewer/2022072016/56649ef65503460f94c0a62b/html5/thumbnails/8.jpg)
1. Find the number of terms in the arithmetic series if:
t1 = 7, tn = -91, Sn = -2100
2. Find the number of term in the geometric series if:
a1 = 6, r = -2, Sn = -8190
Problems #3