- #1
lfdahl
Gold Member
MHB
- 749
- 0
Let $a_1 = 1$, $a_2 = 1$ and $a_n = a_{n-1}+a_{n-2}$ for each $n > 2$. Find the smallest real number, $A$, satisfying
\[\sum_{i = 1}^{k}\frac{1}{a_{i}a_{i+2}} \leq A\]
for any natural number $k$.
\[\sum_{i = 1}^{k}\frac{1}{a_{i}a_{i+2}} \leq A\]
for any natural number $k$.