- #1
daniel_i_l
Gold Member
- 868
- 0
I need to calculate
[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]
[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]
Last edited: