I want to write a general formula of: $$ a_n= a_0\prod^{n}_{i=1} \frac{2i+4}{i(i+1)}$$ I want to write $a_n$ in terms of $n$ only, is this possible?
2026-04-03 05:21:43.1775193703
Eliminate productory
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One may write $$ a_n= a_0\prod^{n}_{i=1} \frac{2i+4}{i(i+1)}=a_0\frac{\prod^{n}_{i=1} 2(i+2)}{\prod^{n}_{i=1} i\prod^{n}_{i=1} (i+1)}=a_0\frac{2^{n}(n+2)!}{2(n!)^2 \cdot (n+1)}=a_0\frac{2^{n-1}(n+2)}{n!}. $$