## aceace Proof Question one year ago one year ago

1. aceace

If $T_{n} = \frac{ n-1 }{ n }$, prove $T_{n+1} - T _{n-1} = \frac{ 2 }{ n^2 -1 }$

2. Mikael

This is nice exercise for the hands

3. Mikael

$T_{n+1} = \frac{n}{n+1}$

4. Mikael

So $T_{n+1} - T_{n-1} = \frac{ n }{ n+1 } - \frac{n-1}{n}$

5. Mikael

Sorry $T_{n+1} - T_{n-1} = \frac{ n }{ n+1 } - \frac{n-2}{n-1}$

6. Mikael

Just bring to the common denominator by multiplying the denominators and recall that $(n+1)(n-1) = ...^2 - 1^2$

7. aceace

it seems like i cant go any further