
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
 LinkBack  Thread Tools  Display Modes 
May 14th, 2018, 05:49 PM  #1 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 1,998 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 05:52 PM. 
May 14th, 2018, 06:17 PM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,771 Thanks: 862  
May 14th, 2018, 10:01 PM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,825 Thanks: 1051 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 10:16 PM. 
May 14th, 2018, 10:48 PM  #4 
Senior Member Joined: Oct 2009 Posts: 430 Thanks: 144  

Tags 
addition, fraction, fracttion 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
fraction addition or product?  Mathis  Algebra  18  December 24th, 2015 02:40 AM 
Algebraic Fraction Addition  Monox D. IFly  Algebra  3  September 11th, 2014 03:53 AM 
How to simplify a fraction times by a fraction  Sammy  Elementary Math  2  August 15th, 2014 02:46 AM 
Basic Algebra, fraction of a fraction...  Tommy_Gun  Algebra  5  June 3rd, 2012 06:14 PM 
Fraction additionwhere is the hole?  arun  Number Theory  15  February 11th, 2007 01:42 PM 