
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
 LinkBack  Thread Tools  Display Modes 
May 14th, 2018, 06:00 PM  #1 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 2,000 Thanks: 132 Math Focus: Trigonometry  [ASK] Fraction Addition with Arithmetic Series as Denominators
Does anyone know how to add these fractions? $\displaystyle \frac11+\frac1{1+2}+\frac1{1+2+3}+…+\frac1{1+2+3 +…+2009}$ Like my previous question, I believe this one also has something which can be canceled out, and the denominators contain arithmetic series. Can this series be used to make some sorts of shortcuts? Last edited by greg1313; May 14th, 2018 at 10:49 PM. 
May 14th, 2018, 10:08 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,879 Thanks: 1087 Math Focus: Elementary mathematics and beyond 
$$\sum_{k=1}^n\frac{2}{k(k+1)}=\frac{2n}{n+1}$$ You can prove it via induction. Last edited by greg1313; May 14th, 2018 at 10:16 PM. 
May 15th, 2018, 05:45 AM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,320 Thanks: 936 
Sum of the reciprocals of the 1st n triangular numbers...


Tags 
addition, arithmetic, denominators, fraction, fracttion, series 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
[ASK] Fraction Addition  Monox D. IFly  Elementary Math  3  May 14th, 2018 10:48 PM 
Series addition of a quadratic  matisolla  Calculus  3  February 28th, 2015 10:17 AM 
Roots Denominators in a Series  Monox D. IFly  Elementary Math  5  August 16th, 2014 01:34 AM 
Arithmetic Series  poochie03  Algebra  1  November 6th, 2011 01:10 PM 
Sum of arithmetic series...  lgchic  Applied Math  1  April 3rd, 2008 05:11 AM 