## anonymous 3 years ago Proof Question

1. anonymous

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

2. anonymous

This is nice exercise for the hands

3. anonymous

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

4. anonymous

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

5. anonymous

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

6. anonymous

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

7. anonymous

it seems like i cant go any further

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