Answer to Question 5

There are 8 discs in the given diagram, so n = 8.
The given recursive formula is based upon the term immediately in front of the term you seek. We need to find our way up to the 8^th entry.
M₁ = 1
M_n = 2M_n-1 + 1

a) M₈ = 2M₇ + 1

1, 3, 7, 15, 31, 63, 127, 255, ...

Answer = 255 moves

b) The number of moves are each one less than a power of 2. It can be expressed as an explicit formula:
M_n = 2ⁿ - 1

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