2009 UNCO Math Contest II Problems/Problem 11

Problem

If the following triangular array of numbers is continued using the pattern established, how many numbers (not how many digits) would there be in the $100^{th}$ row? As an example, the $5^{th}$ row has $11$ numbers. Use exponent notation to express your answer.

$\begin{align*} &1 \\ &2 \\ 3\quad &4\quad 5\quad \\ 6\quad 7\quad &8\quad 9\quad 10\quad \\ 11\quad 12\quad 13\quad 14\quad 15\quad &16\quad 17\quad 18\quad 19\quad 20\quad 21\quad \\ 22\quad 23\quad 24\quad 25\quad 26\quad 27\quad 28\quad 29\quad 30\quad 31\quad &32\quad 33\quad 34 \quad 35\quad 36\quad 37\quad 38\quad 39\quad 40\quad 41\quad 42\quad \\ \cdot \quad &\cdot\quad \cdot\quad \\ \end{align*}$

Solution

$\frac{2^{100}-1}{3}$

2009 UNCO Math Contest II (Problems • Answer Key • Resources)
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2009 UNCO Math Contest II Problems/Problem 11

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