Difference between revisions of "2002 AIME I Problems/Problem 7"
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<cmath>(x+y)^r=x^r+rx^{r-1}y+\dfrac{r(r-1)}{2}x^{r-2}+\dfrac{r(r-1)(r-2)}{3!}x^{r-3}y\cdots</cmath> | <cmath>(x+y)^r=x^r+rx^{r-1}y+\dfrac{r(r-1)}{2}x^{r-2}+\dfrac{r(r-1)(r-2)}{3!}x^{r-3}y\cdots</cmath> | ||
| − | What are the first three digits to the right of the decimal point in the decimal representation of <math>(10^{2002}+1)^{\ | + | What are the first three digits to the right of the decimal point in the decimal representation of <math>(10^{2002}+1)^{\frac{10}{7}}</math>? |
== Solution == | == Solution == | ||
Revision as of 16:34, 25 September 2007
Problem
The Binomial Expansion is valid for exponents that are not integers. That is, for all real numbers 
and 
with 
,
![\[(x+y)^r=x^r+rx^{r-1}y+\dfrac{r(r-1)}{2}x^{r-2}+\dfrac{r(r-1)(r-2)}{3!}x^{r-3}y\cdots\]](http://latex.artofproblemsolving.com/6/0/a/60a4ce8092a322585f952d4db1db5e5e6a0f5663.png)
What are the first three digits to the right of the decimal point in the decimal representation of 
?
Solution
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