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Math Help - What is the value in terms of n (Summation Notation)

  1. #1
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    What is the value in terms of n (Summation Notation)

    ∑_(r=1)^n▒1/(r(r+1))
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  2. #2
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    \begin{aligned}<br />
   \sum\limits_{r=1}^{n}{\frac{1}{r(r+1)}}&=\sum\limi  ts_{r=1}^{n}{\frac{(r+1)-r}{r(r+1)}} \\ <br />
 & =\underbrace{\sum\limits_{r=1}^{n}{\left( \frac{1}{r}-\frac{1}{r+1} \right)}}_{{\text{Telescoping summation}}} \\ <br />
 & =1-\frac{1}{n+1}=\frac{n}{n+1}.<br />
\end{aligned}
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  3. #3
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    = to 1?

    ∑_(r=1 )^n▒1/r= to 1? Why? Which rule?
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