This recurrence solves to T(n) = 2ⁿ − 1.
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- #### 5.48
- Frank is debugging a recursive function that computes Fibonacci numbers. The function runs with time complexity T(n) = 2T(n−1) + 1, with T(1) = 1. What is the value of T(10)?
- Check: T(1) = 2¹ − 1 = 1 ✔️
- T(2) = 2T(1)+1 = 2+1=3; 2²−1=3 ✔️
- T(3) = 2×3+1=7; 2³−1=7 ✔️
