Let Fn be the Fibonacci numbers with F1 F2 Prove Let Fn be

Let Fn be the Fibonacci numbers (with F1 = F2). Prove:

Let Fn be the Fibonacci numbers (with F1 = F2 = 1). Prove that

Solution

This can be proved by taking any value of n and chek if left hand side and right hand side are equal or not.

Let n=5

LHS:

Fibonacci series : 1,1,2,3,5,8,13,21,34,55,89......

5C1*1 + 5C2 *1 + 5C3*2 + 5C4*3 + 5C5*5

= 5 + 10 + 20 + 15 + 5

= 55

RHS:

F(10) = 55 {From fibonacci series}

Hence LHS=RHS

Proved