# Recurrence Relations/Difference Equations

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Solve the following difference equations/recurrence relations:

a)

b)

c)

Kindly show work in detail so I can understand the steps! Thanks!

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#### Solution Preview

Answer:

I assume that n is a natural number and its count starts from 1, that is n = 1, 2, ...

Solutions:

(a) Lets rewrite it as x_{n+1} = n x_n and look at the first few values:

x_1 has some arbitrary value

x_2 = 1 * x_1

x_3 = 2 * x_2 = 2*1 * x_1

x_4 = 3 * x_3 = 3*2*1 * x_1

.....

Here you can already guess that

x_n = (n-1)! * x_1

[You must have already learned about ...

#### Solution Summary

The expert solves recurrence relations and difference equations.

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