Relation Between Pascal triangle and Fibonacci numbers
Pascal’s triangle is the arrangement of the data in triangular form which is used to represent the coefficients of the binomial expansions, i.e. the second row in Pascal’s triangle represents the coefficients in (x+y)2 and so on. In Pascal’s triangle, each number is the sum of the above two numbers. Pascal’s triangle has various applications in probability theory, combinatorics, algebra, and various other branches of mathematics.
As shown in the image the diagonal sum of the pascal’s triangle forms a fibonacci sequence.Mathematically: [Tex]\Sigma_{k=0}^{\left \lfloor n/2 \right \rfloor} \binom{n-k}{k} = F_{n+1} [/Tex]
where [Tex]F_{t} [/Tex] is the t-th term of the Fibonacci sequence.
Fibonacci Series
Ever wondered about the cool math behind the Fibonacci series? This simple pattern has a remarkable presence in nature, from the arrangement of leaves on plants to the spirals of seashells. We’re diving into this Fibonacci Series sequence. It’s not just math, it’s in art, nature, and more! Let’s discover the secrets of the Fibonacci series together.