Property 7
Product Notation
\(\prod\longrightarrow\) pi (product notation).
\(n,r\in\mathbb Z\)
\(\prod\limits_{k=r}^{n}f(k)=f(r)\cdot f(r+1)\cdot f(r+2)\cdot\cdots\cdot f(n)\)
\(k\in\{r,(r+1),(r+2),\ldots,n\}\)
1.
\(\prod\limits_{k=3}^{5}(2k)=?\)
2.
\(\prod\limits_{k=2}^{4}3=?\)
3.
\(\prod\limits_{k=4}^{6}k=?\)
4.
\(\prod\limits_{k=1}^{10}(-1)=?\)
5.
\(\prod\limits_{k=1}^{4}k^2=?\)
6.
\(\prod\limits_{k=3}^{5}(k+2)=?\)
7.
\(\prod\limits_{k=-2}^{-1}k^4=?\)
Property 8
- \(\prod\limits_{k=1}^{n}k=1\cdot2\cdot3\cdot\cdots\cdot n=n!\)
- \(\prod\limits_{k=r}^{n}k=r\cdot(r+1)\cdot\cdots\cdot n=\samefrac{n!}{(r-1)!}\)
1.
\(\prod\limits_{k=1}^{10}k=?\)
2.
\(\prod\limits_{k=2}^{20}k=?\)
3.
\(\prod\limits_{k=7}^{30}k=?\)
4.
\(\prod\limits_{k=10}^{25}k=?\)
5.
\(\prod\limits_{k=7}^{13}k=?\)
6.
\(\prod\limits_{k=-3}^{7}k=?\)