[Maths] Sequences
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Transcript of [Maths] Sequences
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SEQUENCES & SERIES
Miguel Pérez Fontenla, Nov 2009
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1,2,3,4,5,.....
...6,7,8,......
n
Natural numbers
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2,4,6,8,.....
...10,12,14......
Even numbers
2n
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1,3,5,7,.....
...9,11,13......
Odd numbers
2 1n
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4,7,10,13,.....
...16,19,22......
Multiple of three plus one
3 1n
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2,4,8,16,.....
...32,64,128.....
Powers of two
2n
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1,2,4,8,16,.....
...32,64,128.....
Powers of two
12
n
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1,3,9,27,.....
...81,243,.....
Powers of three
13
n
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2,5,10,17,.....
...26,37,.....
n squared plus one
21n
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1,8,27,64,.....
...125,216,.....
n cubed
3n
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2,6,12,20,.....
...56,72,90,.....
n multiplied by n minus one
1n n
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1 1 3, , , ....
2 2 2
2 3
2
n
5 7 9..., , , , ....
2 2 2
two times n minus three divided by two
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-1,1,-1,1,.....
...-1,1,-1,1,.....
minus one to the power of n
1n
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1,-1,1,-1,.....
...1,-1,1,-1,.....
minus one to the power of n plus one
1
1n
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two times n divided by two times n minus one
2 4 6 8, , , ....
1 3 5 7
10 12 14..., , , , ....
9 11 13
2
2 1
n
n
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and....
Other series not so easy
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1,0,1,0,1.....
...0,1,0,1.....1
1 if n odd 1 1
0 if n even 2
n
na
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1,1,2,3,5.....
...8,13,21,.....
Fibonacci Sequence
1 2
1 if n = 1
if n > 1n
n n
aa a
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81,27,9,.....
...3,1,1/3,.....
on divided by 3 to the power of n minus five
5
1
3n
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2,3,5,7,11,.....
...13,17,19,23.....
prime numbers
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0,1,4,6,8,9,10,.....
...12,14,15,16.....
no prime numbers
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2,-4,6,-8.....
...10,-12,14,...
minus one to the power of n plus one multiplied by two times n
1
1 2n
n
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two thirds to the power of n minus five
81 27 9 3, , , , ...
16 8 4 2
5
2 4 8 21, , , ...
3 9 16 3
n
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two tine 2 squared to the power of n minus onedivided by four
1 2, , 2, ...
4 2
1
2 2
4 2 ,16, 32 2 , ...4
n
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and now....
Funny series
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a,b,d,g,k.....
...p,v,...
following the sequence 1,2,4,7,11,16,22
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O,T,T,F,F,S,S.....
...,E,N,T
One, two, three, four, five,six, seven, eight, nine, ten....
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M,T,W,T,F.....
...S,S
Week days
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M,V,E,M,J.....
...S,N,U,P
Planets Solar SystemMercury, Venus, Earth, Mars, Jupiter, Saturn, Neptune, Uranus,
Pluto
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F,S,T,F,F,S,S..... ,E,N,T
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J,F,M,A,M,J,J........,A,S,O,N,D
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31,28,31,30,31,...
...30,31,31,..Lengths of months in days
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2,2,4,4,2,6,6,2,8,...
...8,2,10,...Table of two
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5,4,2,9,8,6,...
...7,3,1Alphabetic Order In Spanish
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2,10,12,16,17,18,19,200...
...201,202,..
In Spanish they start by the “D” letter:Dos, diez, doce, dieciseis,
diecisiete,dieciocho,diecinueve,doscientos....
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2,3,6,16,22,23,26,32,33...
...36,42,43,46,..
In Spanish they finish with the “S” letter:Dos, tres, seis, dieciseis, veintidos, veintitres, veintiseis,
treinta y dos ....