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 

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