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1 solution
We notice that the sum of the first two terms cancel. Then, the sum of the first two terms and the next four terms cancel. Then, the sum of the first two terms, the next four terms, and the next 6 terms cancel. Continuing on this way, the sum of the first:
2 + 4 + 6 + 8 + ... + 2*k
terms will cancel. But, we see that:
2 + 4 + 6 + 8 + ... + 2 k = 2 k(k+1)/2 = k*(k+1)
When k = 31, this expression is 992. In other words, the sum of the first 992 terms will cancel. The remaining 8 terms are 1, 2, 3, 4, ..., 8, and the sum of these terms is 8*9/2 = 36