Difference between revisions of "2002 AIME I Problems/Problem 7"
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== Problem == | == Problem == | ||
| + | The Binomial Expansion is valid for exponents that are not integers. That is, for all real numbers <math>x,y</math> and <math>r</math> with <math>|x|>|y|</math>, | ||
| + | |||
| + | <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)^{\dfrac{10}{7}}</math>? | ||
== Solution == | == Solution == | ||
Revision as of 15:34, 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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