2011 UNCO Math Contest II Problems/Problem 7

Revision as of 03:22, 13 January 2019 by Timneh (talk | contribs) (Solution)

Problem

What is the $\underline{sum}$ of the first $999$ terms of the sequence $1, 2, 3, 6, 7, 14, 15, 30, 31, 62, 63,\cdots$ 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.

Solution

$2^{502}-1504$

See Also

2011 UNCO Math Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 6
Followed by
Problem 8
1 2 3 4 5 6 7 8 9 10
All UNCO Math Contest Problems and Solutions
Invalid username
Login to AoPS