Difference between revisions of "2004 AMC 12A Problems/Problem 21"
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== Problem == | == Problem == | ||
| − | If <math>\sum_{n = 0}^{\infty}{\cos^{2n}\theta = 5</math>, what is the value of <math>\cos{2\theta}</math>? | + | If <math>\sum_{n = 0}^{\infty}{\cos^{2n}}\theta = 5</math>, what is the value of <math>\cos{2\theta}</math>? |
<math>\text {(A)} \frac15 \qquad \text {(B)} \frac25 \qquad \text {(C)} \frac {\sqrt5}{5}\qquad \text {(D)} \frac35 \qquad \text {(E)}\frac45</math> | <math>\text {(A)} \frac15 \qquad \text {(B)} \frac25 \qquad \text {(C)} \frac {\sqrt5}{5}\qquad \text {(D)} \frac35 \qquad \text {(E)}\frac45</math> | ||
Revision as of 18:07, 6 July 2015
Problem
If 
, what is the value of 
?
Solution
This is an infinite geometric series, which sums to 
. Using the formula 
.
See also
| 2004 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 20 |
Followed by Problem 22 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
