That has saved us all a lot of trouble! Thank you Leonardo.įibonacci Day is November 23rd, as it has the digits "1, 1, 2, 3" which is part of the sequence. "Fibonacci" was his nickname, which roughly means "Son of Bonacci".Īs well as being famous for the Fibonacci Sequence, he helped spread Hindu-Arabic Numerals (like our present numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9) through Europe in place of Roman Numerals (I, II, III, IV, V, etc). The next number is found by adding up the two numbers before it: the 2. His real name was Leonardo Pisano Bogollo, and he lived between 11 in Italy. The Fibonacci Sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34. as well as expand our services into AP Calculus AB & BC, AP. Sequences are in nite lists of numbersa1 a2 a3 : : : an : :. Historyįibonacci was not the first to know about the sequence, it was known in India hundreds of years before! be an invaluable resource as you are studying for your Algebra 2 Regents examination. DeTurck University of Pennsylvania MaSequences The lists of numbers you generate using a numerical method likeNewtons method to get better and better approximations to theroot of an equation are examples of (mathematical) sequences. Other Useful facts a nconverges to zero if and only if ja njalso converges to zero. 3 removable discontinuity, 132 resources, Internet Cheat Sheet. The AP Calculus AB and BC exams are coming up, these review charts and cheat sheets will make sure you have everything you need to prepare. Sequence: a list of numbers which is ordered Squeeze/Pinch/Sandwich Theorem If lim. 91 geometry, 5960 improper integrals, 575 infinite series, 616 integrals. Squeeze theorem If b n a n c nfor all values of n, and limb n limc n L, then it implies that lima n L. Calculus 2 Series and Sequences Review Sheet Sequences and Series. Which says that term "ân" is equal to (â1) n+1 times term "n", and the value (â1) n+1 neatly makes the correct +1, â1, +1, â1. Review Sheet for Calculus 2 Sequences and Series SEQUENCES Convergence A sequence fa ngconverges if lima nexists and is nite. In fact the sequence below zero has the same numbers as the sequence above zero, except they follow a +-+. We say the sequence fangconverges to L and write lim n an L or anL as n if for everye> 0, there exists M such thatjanLj M.ââ.(Prove to yourself that each number is found by adding up the two numbers before it!) Asequenceis a function with domainN f1,2,3.g, the Natural Numbers.
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