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[Maths] Sequences 03

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miguelperezfontenla

The document lists and describes various types of sequences and series, including: 1) Natural numbers, even numbers, odd numbers, multiples of three plus one, powers of two, powers of three, numbers squared plus one, numbers cubed, and numbers multiplied by numbers minus one. 2) Other series include the Fibonacci sequence, numbers divided by three to the power of n minus five, prime numbers, and minus one to the power of n plus one multiplied by two times n. 3) Funny series include sequences following patterns like the alphabet, days of the week, months of the year, and numbers in Spanish starting or ending with certain letters.

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SEQUENCES & SERIES Miguel Pérez Fontenla, Nov 2009
1,2,3,4,5,..... ...6,7,8,...... Natural numbers
2,4,6,8,..... ...10,12,14...... Even numbers
1,3,5,7,..... ...9,11,13...... Odd numbers
4,7,10,13,..... ...16,19,22...... Multiple of three plus one
2,4,8,16,..... ...32,64,128..... Powers of two
1,2,4,8,16,..... ...32,64,128..... Powers of two
1,3,9,27,..... ...81,243,..... Powers of three
2,5,10,17,..... ...26,37,..... n squared plus one
1,8,27,64,..... ...125,216,..... n cubed
2,6,12,20,..... ...56,72,90,..... n multiplied by n minus one
two times n minus three divided by two
-1,1,-1,1,..... ...-1,1,-1,1,..... minus one to the power of n
1,-1,1,-1,..... ...1,-1,1,-1,..... minus one to the power of n plus one
two times n divided by two times n minus one
and.... Other series not so easy
1,0,1,0,1..... ...0,1,0,1.....
1,1,2,3,5..... ...8,13,21,..... Fibonacci Sequence
81,27,9,..... ...3,1,1/3,..... on divided by 3 to the power of n minus five
2,3,5,7,11,..... ...13,17,19,23..... prime numbers
0,1,4,6,8,9,10,..... ...12,14,15,16..... no prime numbers
2,-4,6,-8..... ...10,-12,14,... minus one to the power of n plus one multiplied by two times n
two thirds to the power of n minus five
two tine 2 squared to the power of n minus one divided by four
and now.... Funny series
a,b,d,g,k..... ...p,v,... following the sequence 1,2,4,7,11,16,22
O,T,T,F,F,S,S..... ...,E,N,T One, two, three, four, five, six, seven, eight, nine, ten....
M,T,W,T,F..... ...S,S Week days
M,V,E,M,J..... ...S,N,U,P Planets Solar System Mercury, Venus, Earth, Mars, Jupiter, Saturn, Neptune, Uranus, Pluto
F,S,T,F,F,S,S..... ,E,N,T
J,F,M,A,M,J,J..... ...,A,S,O,N,D
31,28,31,30,31,... ...30,31,31,.. Lengths of months in days
2,2,4,4,2,6,6,2,8,... ...8,2,10,... Table of two
5,4,2,9,8,6,... ...7,3,1 Alphabetic Order In Spanish
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....
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 ....

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