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1998 PMWC Problems/Problem I1

Revision as of 16:36, 8 August 2009 by Ihatepie (talk | contribs) (Created page with '== Problem I1 == Calculate: <math>\frac{1*2*3+2*4*6+3*6*9+4*8*12+5*10*15}{1*3*5+2*6*10+3*9*15+4*12*20+5*15*25}</math> == Solution == If you factor the top, you get <math>(1*2*3…')
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Problem I1

Calculate: $\frac{1*2*3+2*4*6+3*6*9+4*8*12+5*10*15}{1*3*5+2*6*10+3*9*15+4*12*20+5*15*25}$

Solution

If you factor the top, you get $(1*2*3)(1^{3}+2^{3}+3^{3}+4^{3}+5^{3})$


If you factor the bottom, you get $(1*3*5)(1^{3}+2^{3}+3^{3}+4^{3}+5^{3})$

Dividing out the common factor, you get \[\frac {1*2*3}{1*3*5}\] \[\frac {6}{15}\] \[\frac {2}{5}\]

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