2011 UNCO Math Contest II Problems/Problem 7
What is the of the first terms of the sequence that appeared on the First Round? Recall that a term in an even numbered position is twice the previous term, while a term in an odd numbered position is one more that the previous term.
Group every even term with the term following it, like so
Since every odd term is 1 less than a power of two, we know each group will be of the form , or just . So our sum becomes
Counting yields 500 such groups, leaving us with a geometric series minus , giving us
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