Binet`s formula for Fibonacci numbers
... frequent occurrence in nature. Take flowers, for example. Consistently, the number of petals in a daisy is a Fibonacci number, which depends on the variety: 13 for Blue daisies; 21 for English daisies; 34 for Oxeye daisies; 55 for African daisies, and so on. What's true for daisies is also true for ...
... frequent occurrence in nature. Take flowers, for example. Consistently, the number of petals in a daisy is a Fibonacci number, which depends on the variety: 13 for Blue daisies; 21 for English daisies; 34 for Oxeye daisies; 55 for African daisies, and so on. What's true for daisies is also true for ...
Full text
... Since then, several authors proved general theorems on fractions that can be represented as series Involving Fibonacci numbers and general n-Bonacci numbers [1, 2, 3, 4 ] . In the present paper we will prove a theorem which includes as special cases all the earlier results. We introduce some notatio ...
... Since then, several authors proved general theorems on fractions that can be represented as series Involving Fibonacci numbers and general n-Bonacci numbers [1, 2, 3, 4 ] . In the present paper we will prove a theorem which includes as special cases all the earlier results. We introduce some notatio ...
Continued Fraction Notes (Merry Christmas!)
... But it is easy to check that this number is between B and n since this is true for all n, it follows that α is the limit! ...
... But it is easy to check that this number is between B and n since this is true for all n, it follows that α is the limit! ...
A10 Generating sequences
... Writing sequences from position-to-term rules The position-to-term rule for a sequence is very useful because it allows us to work out any term in the sequence without having to work out any other terms. We can use algebraic shorthand to do this. We call the first term T(1), for Term number 1, we c ...
... Writing sequences from position-to-term rules The position-to-term rule for a sequence is very useful because it allows us to work out any term in the sequence without having to work out any other terms. We can use algebraic shorthand to do this. We call the first term T(1), for Term number 1, we c ...
1.1A Arithmetic Sequences
... It contains elements or terms that follow a pattern or rule to determine the next term in the sequence. The numbers in sequences are called terms. ...
... It contains elements or terms that follow a pattern or rule to determine the next term in the sequence. The numbers in sequences are called terms. ...
download_pptx
... Is it true that x³ is O(7x²)? Determine whether witnesses exist or not. Assume we can find C and k such that x³≤C(7x²) whenever x>k i.e. x≤7C whenever x>k No matter what C and k are, the inequality x≤7C cannot hold for all x with x>k. ◦ So, x³ is not O(7x²). ...
... Is it true that x³ is O(7x²)? Determine whether witnesses exist or not. Assume we can find C and k such that x³≤C(7x²) whenever x>k i.e. x≤7C whenever x>k No matter what C and k are, the inequality x≤7C cannot hold for all x with x>k. ◦ So, x³ is not O(7x²). ...