Property 11
\(\prod_{k=r}^{n}f(k)=\samefrac{\prod_{k=1}^{n}f(k)}{\prod_{k=1}^{r-1}f(k)}\)
\(\prod_{k=r}^{n}f(k)=\prod_{k=r+a}^{n+a}f(k-a)\)
\(\prod_{k=r}^{n}f(k)=\prod_{k=r-a}^{n-a}f(k+a)\)
1.
\(\prod_{k=3}^{10}(k-2)=?\)
2.
\(\prod_{k=-4}^{17}(k+5)=?\)
3.
\(\prod_{k=-3}^{10}(2k+8)=?\)
4.
\(\prod_{k=-5}^{12}(3k+18)=?\)
5.
\(\prod_{k=-2}^{11}(k^2-1)=?\)
Property 12
\(\prod_{k=r}^{n}c^{f(k)}=c^{f(r)}c^{f(r+1)}\cdots c^{f(n)}=c^{\sum_{k=r}^{n}f(k)}\)
1.
\(\prod_{k=1}^{10}2^k=?\)
2.
\(\prod_{k=4}^{20}3^{k-3}=?\)
3.
\(\prod_{k=1}^{15}\left(\samefrac14\right)^k=?\)
4.
\(\prod_{k=2}^{12}3^{k^2-1}=?\)
5.
\(\prod_{k=1}^{11}\sqrt{6^k}=?\)