Question

\[a_{n+2}=\frac{a_n}{(n+1)(n+2)}\]
\[a_9=\frac{a_7}{8\cdot9}=\frac{a_0}{2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9}\]

Answer 1

\[y=\sum_{\infty}^{n=0}\]

Answer 2

....

Answer 3

@phi please help

Answer 4

after some thinking I decided that \( a_n= \frac{a_0}{n!} \)
and you want
\[\sum_{n=0}^{\infty}\frac{a_0}{n!}= a_0\sum_{n=0}^{\infty}\frac{1}{n!}\]
See
http://www.khanacademy.org/math/calculus/integral-calculus/v/approximating-functions-with-polynomials--part-3