Sequences and Series by Maluleke PJ
-
Upload
ponani-jackson-maluleke -
Category
Education
-
view
117 -
download
2
Transcript of Sequences and Series by Maluleke PJ
![Page 1: Sequences and Series by Maluleke PJ](https://reader035.fdocuments.net/reader035/viewer/2022062708/5589605cd8b42a4d718b46a9/html5/thumbnails/1.jpg)
SEQUENCES AND
SERIES(ARITHMETIC)BY MALULEKE PJ
![Page 2: Sequences and Series by Maluleke PJ](https://reader035.fdocuments.net/reader035/viewer/2022062708/5589605cd8b42a4d718b46a9/html5/thumbnails/2.jpg)
SUM MATHEMATICIAN
•CARL FRIEDRICH GAUSS
![Page 3: Sequences and Series by Maluleke PJ](https://reader035.fdocuments.net/reader035/viewer/2022062708/5589605cd8b42a4d718b46a9/html5/thumbnails/3.jpg)
• NATURE---DID YOU KNOW: UNDERSTANDING A SEQUENCE, ILLUSTRATED BELOW IS A FIBONACCI SEQUENCE ONE OF THE ANCIENT PATTERNS TO EVER BEING DISCOVERED BY MAN-KIND(JACOBS,2011)
![Page 4: Sequences and Series by Maluleke PJ](https://reader035.fdocuments.net/reader035/viewer/2022062708/5589605cd8b42a4d718b46a9/html5/thumbnails/4.jpg)
ARITHMETIC SEQUENCE•RIMANDO:IT IS A SEQUENCE IN WHICH THE DIFFERENCE BETWEEN CONSECUTIVE TERMS IS CONSTANT AND HAS THE FORM:
• NOTE: AN ARITHMETIC
SEQUENCE
• EXHIBIT CONSTANT GROWTH
dnadadaa 1,,2,, 1111
![Page 5: Sequences and Series by Maluleke PJ](https://reader035.fdocuments.net/reader035/viewer/2022062708/5589605cd8b42a4d718b46a9/html5/thumbnails/5.jpg)
ARITHMETIC SEQUENCE•EXAMPLES:
• 1, 4, 7, 10, 13, …
• 6, 11, 16, 21, 26, …
• 14, 25, 36, 47, 58, …
• 4, 2, 0, -2, -4, …
• -1, -7, -13, -19, -25, …
![Page 6: Sequences and Series by Maluleke PJ](https://reader035.fdocuments.net/reader035/viewer/2022062708/5589605cd8b42a4d718b46a9/html5/thumbnails/6.jpg)
ARITHMETIC SEQUENCE
•GENERAL TERM:
dnaan 11
![Page 7: Sequences and Series by Maluleke PJ](https://reader035.fdocuments.net/reader035/viewer/2022062708/5589605cd8b42a4d718b46a9/html5/thumbnails/7.jpg)
Example/s:
Find the 50th term of the arithmetic sequence 2, 6, 10, 14, …
![Page 8: Sequences and Series by Maluleke PJ](https://reader035.fdocuments.net/reader035/viewer/2022062708/5589605cd8b42a4d718b46a9/html5/thumbnails/8.jpg)
ARITHMETIC SERIES•A SERIES IS AN INDICATED SUM OF TERMS OF A SEQUENCE. IF THE TERMS FORM AN ARITHMETIC
SEQUENCE WITH FIRST TERM A1
AND COMMON DIFFERENCE D, THE INDICATED SUM OF TERMS IS CALLED AN ARITHMETIC SERIES. THE SUM OF THE FIRST N TERMS,
REPRESENTED AS SN,
IS(GAUTANI,2011)nnn aaaaaS 1321
![Page 9: Sequences and Series by Maluleke PJ](https://reader035.fdocuments.net/reader035/viewer/2022062708/5589605cd8b42a4d718b46a9/html5/thumbnails/9.jpg)
ARITHMETIC SERIES•LET SN = A1 + A2 + … +
AN BE AN ARITHMETIC
SERIES WITH CONSTANT DIFFERENCE D, THEN:
2
12 1 dnanSn
![Page 10: Sequences and Series by Maluleke PJ](https://reader035.fdocuments.net/reader035/viewer/2022062708/5589605cd8b42a4d718b46a9/html5/thumbnails/10.jpg)
ARITHMETIC SERIES•LET SN = A1 + A2 + … +
AN BE AN ARITHMETIC
SERIES THEN 21 n
n
aanS
![Page 11: Sequences and Series by Maluleke PJ](https://reader035.fdocuments.net/reader035/viewer/2022062708/5589605cd8b42a4d718b46a9/html5/thumbnails/11.jpg)
Example/s:
Find the sum of the first 100 positive even numbers.
![Page 12: Sequences and Series by Maluleke PJ](https://reader035.fdocuments.net/reader035/viewer/2022062708/5589605cd8b42a4d718b46a9/html5/thumbnails/12.jpg)
Reference: Rimando, K. (2011), Sequences and SeriesJacobs, J. (2011), Patterns and SequencesGautani, V. (2011), Sequences and series and binomial TheoremImages: @windows7, Wikipedia