I can prove the base case and get that $1/3=1/3$, but i can't get any further with the $n+1$ case. Can someone help me?
I was told to conjecture a formula for the sum $\frac{1}{3} + \frac{1}{{3 \cdot 5}} + \cdots + \frac{1}{{\left( {2n - 1} \right)\left( {2n + 1} \right)}}$ I thought I figured out that this sum was equal to $\frac{1}{2} { - \frac{1}{{4n + 2}}} $ but I'm starting to think I'm wrong about that. After we have the formula, we were told to prove our conjecture using induction.