## aceace Group Title If T_{n} = \frac{ n-1 }{ n } , prove T_{n+1} - T _{n-1} = \frac{ 2 }{ n^2 -1 } one year ago one year ago

1. aceace Group Title

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

2. KingGeorge Group Title

First, you want to write out what $$T_{n+1}$$ and $$T_{n-1}$$ are using the fact that $$\displaystyle T_n=\frac{n-1}{n}$$. Can you tell me what $$T_{n+1}$$ is?

3. aceace Group Title

n/n+1

4. KingGeorge Group Title

Right, and $$T_{n-1}$$?

5. aceace Group Title

n-2/n-1

6. KingGeorge Group Title

Bingo. So you have $T_{n+1}-T_{n-1}=\frac{n}{n+1}-\frac{n-2}{n-1}$Find a common denominator, and simplify.

7. aceace Group Title

yeh i did that and got to the answer 2/(1-n) which is wrong

8. KingGeorge Group Title

Alright, to get a common denominator, you do the following, and simplify. $\left(\frac{n}{n+1}\cdot\frac{n-1}{n-1}\right)-\left(\frac{n-2}{n-1}\cdot\frac{n+1}{n+1}\right)$ Does this help?

9. aceace Group Title

just a sec

10. aceace Group Title

yeh i got that step except i cant get the final answer

11. aceace Group Title