Starting with number 3, repeat 30 times the operation of doubling and…
2026
Starting with number 3, repeat 30 times the operation of doubling and subtracting 1, then what will you get
Answer: A. 2^31+1 — Define a_0 = 3 and for each n define a_{n+1} = 2*a_n - 1. Base case: For n = 0, a_0 = 3 = 2^1 + 1. Inductive step: Assume a_n = 2^{n+1} + 1. Then a_{n+1} =…
- A.
2^31+1
- B.
3*2^31
- C.
2^31-1
- D.
3*2^30
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Correct answer: A
Define a_0 = 3 and for each n define a_{n+1} = 2*a_n - 1.
Base case:
For n = 0, a_0 = 3 = 2^1 + 1.
Inductive step:
Assume a_n = 2^{n+1} + 1. Then
a_{n+1} = 2*a_n - 1 = 2*(2^{n+1} + 1) - 1 = 2^{n+2} + 1.
By induction, after k operations the value is a_k = 2^{k+1} + 1.
For 30 repetitions (k = 30) the result is 2^31+1.
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