A summation of a series based on the Fibonacci sequence.
Hint: prove by induction that $\sum_{i=1}^{n}\frac{1}{a_{2i-1}a_{2i+1}} = \frac{F_{2n}}{a(F_{2n-1} a+F_{2n}b)}$
Hint: prove by induction that $\sum_{i=1}^{n}\frac{1}{a_{2i-1}a_{2i+1}} = \frac{F_{2n}}{a(F_{2n-1} a+F_{2n}b)}$