Sequences and Series by Maluleke PJ
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Transcript of Sequences and Series by Maluleke PJ
SEQUENCES AND
SERIES(ARITHMETIC)BY MALULEKE PJ
SUM MATHEMATICIAN
•CARL FRIEDRICH GAUSS
• 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)
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
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, …
ARITHMETIC SEQUENCE
•GENERAL TERM:
dnaan 11
Example/s:
Find the 50th term of the arithmetic sequence 2, 6, 10, 14, …
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
ARITHMETIC SERIES•LET SN = A1 + A2 + … +
AN BE AN ARITHMETIC
SERIES WITH CONSTANT DIFFERENCE D, THEN:
2
12 1 dnanSn
ARITHMETIC SERIES•LET SN = A1 + A2 + … +
AN BE AN ARITHMETIC
SERIES THEN 21 n
n
aanS
Example/s:
Find the sum of the first 100 positive even numbers.
Reference: Rimando, K. (2011), Sequences and SeriesJacobs, J. (2011), Patterns and SequencesGautani, V. (2011), Sequences and series and binomial TheoremImages: @windows7, Wikipedia