Bunuel wrote:
\(S_n=\frac{-1}{S_{n-1}+1}\) for all integer values of n greater than 1. If S1 = 1, what is the sum of the first 61 terms in the sequence?
(A) –48
(B) –31
(C) –29
(D) 1
(E) 30
Let’s determine the values of the first few terms of the sequence.
s(1) = 1
s(2) = -1/(1+1) = -½
s(3) = -1/(-½ + 1) = -1/(1/2) = -2
s(4) = -1/(-2 + 1) = -1/-1 = 1
We see that the terms repeat themselves in a cycle of 3 that has a pattern of 1, -1/2, -2, which sum to -1.5. We see that the sum of terms 1-3 is -1.5,
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