Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 May 14th, 2018, 06:49 PM #1 Senior Member     Joined: Nov 2010 From: Indonesia Posts: 2,001 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. I-Fly; May 14th, 2018 at 06:52 PM.
 May 14th, 2018, 07:17 PM #2 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,804 Thanks: 970
 May 14th, 2018, 11:01 PM #3 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,900 Thanks: 1094 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
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Quote:
 Originally Posted by greg1313 $$\sum_{k=1}^n\frac{1}{k(k+1)}=\frac{n}{n+1}$$ You can prove it via induction.
Or use telescoping series and
$$\frac{1}{k(k+1)} = \frac{1}{k} - \frac{1}{k+1}$$

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