1. Recursion and Recurrence Relations
An Introduction

2. Recursion
A technique of defining a function, a set or an algorithm in terms of itself is a “recursion”.
For Example:
Factorial !n=n X !(n-1), and !0=!1=1
Fibonacci sequence f0 =1, f1 =1 and fk =fk-2 +fk-1 for k≥2

3. Solution of a problem with recursion and Iteration
Lets solve this problem with to methods
Recursion
Iteration
Telescoping form of a polynomial expression
Eg. X5 + 3x4 – 15x2 +x -10
Its telescoping form is
(((x((x)+3)))x-15)x+1)x-10

4. Types of Recurrence Relation
Linear Recurrence relation with constant coefficients.
c0 ar + c1 ar-1 + c2 ar-2 + ……..+ ck ar-k =f(r)
Homogeneous recurrence Relation
s(k)+c1 s(k-1) +c2 s(k-2)+…….+ cn s(k-n)=f(k) and f(n)=0
Non-Homogeneous recurrence Relation
s(k)+c1 s(k-1) +c2 s(k-2)+…….+ cn s(k-n)=f(k) and f(n)=non-zero.