Consider the Recurrence Relation $a _ { n } = 2 a _ { n - 1 } + 1$

Short Answer

Consider the recurrence relation $a _ { n } = 2 a _ { n - 1 } + 1$ (a) Write the associated homogeneous recurrence relation. (b) Find the general solution to the associated homogeneous recurrence relation. (c) Find a particular solution to the given recurrence relation. (d) Write the general solution to the given recurrence relation. (e) Find the particular solution to the given recurrence relation when a0 = 1.