
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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May 14th, 2018, 06:49 PM  #1 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 2,000 Thanks: 132 Math Focus: Trigonometry  [ASK] Fraction Addition
Does anyone know how to add these fractions? $\displaystyle \frac1{1\times2}+\frac1{2\times3}+\frac1{3\times4} +…+\frac1{2009\times2010}$ I believe making them in $\displaystyle \frac12+\frac1{6}+\frac1{12}+….+\frac1{421890}$ form isn’t the correct approach. Is there anything we can cancel out? Last edited by Monox D. IFly; May 14th, 2018 at 06:52 PM. 
May 14th, 2018, 07:17 PM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,444 Thanks: 946  
May 14th, 2018, 11:01 PM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,881 Thanks: 1088 Math Focus: Elementary mathematics and beyond 
$$\sum_{k=1}^n\frac{1}{k(k+1)}=\frac{n}{n+1}$$ You can prove it via induction. Last edited by greg1313; May 14th, 2018 at 11:16 PM. 
May 14th, 2018, 11:48 PM  #4 
Senior Member Joined: Oct 2009 Posts: 608 Thanks: 186  

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