2005 AIME II Problems/Problem 7
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Problem
Let Find
.
Solution 1
We note that in general,
.
It now becomes apparent that if we multiply the numerator and denominator of by
, the denominator will telescope to
, so
.
It follows that .
Solution 2 (Bashing)
Let , then eypanding the denominator results in:
Therefore:
It is evident that as Solution 1 states.
See Also
2005 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
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