Institutions: Global | TUT | UCT | UJ | UZ | Wits

10 views
The sequence ${a0, a1, a2, . . .}$ of real numbers satisfies the recursive relation

$$n(n + 1)a_{n+1} + (n − 2)a_{n−1} = n(n − 1)a_{n}$$

for every positive integer $n$, where $a_0 = a_1 = 1$.

Calculate the sum

$$\dfrac{a_0}{ a_1} + \dfrac{a_1}{ a_2} + · · · + \dfrac{a_{2008}}{ a_{2009} }$$
| 10 views