I need to calculate(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\sum_{i=1}^n \frac{1}{i(i+1)}

[/tex]

useing the fact that:

[tex]

\sum_{i=1}^n F(i) - F(i-1) = F(n) - F(0)

[/tex]

now I chose the function

[tex]

F(i) = \frac{1}{i} \frac{1}{(i+1)} ... \frac{1}{(i+r)}

[/tex]

so

[tex]

F(i)-F(i-1)=(\frac{1}{i}\frac{1}{(i+1)} ... \frac{1}{(i+r-1)})(\frac{1}{(i+r)}-\frac{1}{(i-1)})

[/tex]

now I want to use that to calcualte the sum chooseing r as 2, but I'm stuck because the F(0) is undefined, and because of the

[tex]

\frac{1}{i+r}-\frac{1}{i-1})

[/tex]

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# Homework Help: Calculate sums math problem

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