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given a recursive alogrithmn for computing 2^n , n greater than or equal to zero integer,...

given a recursive alogrithmn for computing 2^n , n greater than or equal to zero integer, based on the formula 2^n = 2^n-1 Set up a recurrence relation for the number of additions made by the alogrithmn, and then solve it,

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Answer #1 
recurrence relation:
----------------------
T(n) = T(n-1) + 1
and T(1) = 1

solving recurrence relation:
------------------------------
T(n)
= T(n-1) + 1
= T(n-2) + 1 + 1
= T(n-3) + 1 + 1 + 1
= T(2) + ... + 1 + 1 + 1
= T(1) + 1 + ... + 1 + 1 + 1
= 1 + 1 + ... + 1 + 1 + 1   (n terms)
= n

so, T(n) = n
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