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Explain in Detail :Meaning of Recurrence Relation
A recurrence relation is a mathematical equation that describes the relationship between a sequence of numbers and the sequence of its derivatives. A recurrence relation can be used to calculate the nth term in a sequence, given the first few terms in the sequence.
Methods of Solving Recurrence Relations
There are a few methods to solving recurrence relations. The first is the substitution method. This method substitutes a known value for an unknown in the recurrence relation, and then solves for the unknown. The second is the induction method. This method uses mathematical induction to prove a recurrence relation. The third is the recursion method. This method uses the recurrence relation to derive a formula for the function represented by the recurrence relation.
Examples of Recurrence Relation
Some examples of recurrence relation are:
1) The Fibonacci sequence is a recurrence relation in which each number is the sum of the previous two.
2) The Catalan sequence is a recurrence relation in which each number is the sum of the previous two, excluding the first number.
3) The Pell sequence is a recurrence relation in which each number is the sum of the previous two, excluding the first two numbers.
