Difference between revisions of "2009 UNCO Math Contest II Problems/Problem 11"

(Created page with "== 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 <math>100^{th...")
 
(Solution)
 
(2 intermediate revisions by the same user not shown)
Line 17: Line 17:
  
 
== Solution ==
 
== Solution ==
 +
<math>\frac{2^{100}-1}{3}</math>
  
 
== See also ==
 
== See also ==
{{UNC Math Contest box|year=2009|n=II|num-b=10|after=Last Question}}
+
{{UNCO Math Contest box|year=2009|n=II|num-b=10|after=Last Question}}
  
 
[[Category:Intermediate Algebra Problems]]
 
[[Category:Intermediate Algebra Problems]]

Latest revision as of 01:00, 13 January 2019

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

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

See also

2009 UNCO Math Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 10
Followed by
Last Question
1 2 3 4 5 6 7 8 9 10
All UNCO Math Contest Problems and Solutions