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We are given a recurrence relation: $$ a_n = 2a_{n-1} + 1 \quad \text{for } n \geq 1, \quad \text{with } a_0 = 0 $$ We are to solve this using generating functions and then find $a_5$. --- ### Step 1: Define the generating function Let: $$ A(x) = \sum_{n=0}^{\infty} a_n x^n $$ We will now use the recurrence relation to find an equation involving $A(x)$. --- ### Step 2: Use _______ ______ _________ ___ ____.
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