Difference between revisions of "The Apple Method"
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Solving, we get <math>\textcolor{red}{(\textcolor{green}{^{^(}})}=\boxed{3}</math> | Solving, we get <math>\textcolor{red}{(\textcolor{green}{^{^(}})}=\boxed{3}</math> | ||
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| + | 2. Evaluate: <cmath>\frac{1^2+2^2+3^2+\cdots}{1^2+3^3+5^2+\cdots}</cmath> | ||
Revision as of 22:23, 24 March 2020
The Apple Method is a method for solving algebra problems. An apple is used to make a clever algebraic substitution.
Examples
1. Evaluate: ![\[\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}\]](http://latex.artofproblemsolving.com/b/a/9/ba931c757fe2ab64fb02b7b34de5a0e22ea0b44c.png)
If we set 
, we can see that 
.
Solving, we get 
2. Evaluate: ![\[\frac{1^2+2^2+3^2+\cdots}{1^2+3^3+5^2+\cdots}\]](http://latex.artofproblemsolving.com/5/1/e/51ebeab998a84de66e0d06d6d48891f9b18f1820.png)
