![]() Sequences and Series are used in many fields of engineering.Ĭalculus is one of the greatest achievements of the human mind separately invented by Newton and Leibniz. Public domain image from the Wikimedia Commons The Fibonacci series is used in computer search algorithms, and in biology they describe the pattern of pine cones and flowering of artichokes.Īn approximation of the golden spiral created by drawing circular arcs connecting the opposite corners of squares whose side lengths are successive Fibonacci numbers. ![]() The Fibonacci series is the series where each subsequent number is the sum of the previous two or F n = F n-1 + F n-2 . Where the Greek letter sigma ∑ is the mathematical symbol for a sum, or the summation operator. How many grains are placed on an 8×8 chessboard? Since this is a geometric series, the answer for n squares is so for n = 8 x 8= 64 squares, the total number of grains of wheat = 2 64 - 1. We are concerned with two main types of series or sequences of numbers: Arithmetic series were the difference between any two consecutive terms is a constant, and geometric series were the ratio of any two consecutive terms is always the same.Ī well-known example of a geometric series is the ‘Wheat and Chessboard Problem’: Let one grain of wheat be placed on the first square of a chessboard, two on the second, four on the third, eight on the fourth, etc.
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