Solve the recurrence relation, Mathematics

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Solve the recurrence relation

T (K) = 2T (K-1), T (0) = 1

Ans: The following equation can be written in the subsequent form:

t_n - 2t_n-1 = 0

Here now successively replacing n by (n - 1) and then by (n - 2) and so on we obtain a set of equations.

The method is continued till terminating condition. Add these equations in such type of a way that all intermediate terms get cancelled. The equation can be rearranged as

1709_Solve the recurrence relation.png

Multiplying all the equations correspondingly by 2⁰, 2¹, ..., 2^{n - 1} and then adding them together, we get

t_n - 2ⁿt₀ = 0

or, t_n = 2_n

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