Property 2
Summation Notation
\(\sum\) is sigma (summation notation).
\(\sum_{k=r}^{n}f(k)=f(r)+f(r+1)+\cdots+f(n)\)
\(k\in\{r,r+1,\ldots,n\}\)
\(\sum_{k=1}^{n}k=\samefrac{n(n+1)}2\)
\(\sum_{k=1}^{n}k^2=\samefrac{n(n+1)(2n+1)}6\)
\(\sum_{k=1}^{n}k^3=\left[\samefrac{n(n+1)}2\right]^2\)
1.
\(\sum_{k=3}^{5}k^2=?\)
2.
\(\sum_{k=2}^{6}(2k)=?\)
3.
\(\sum_{k=1}^{5}7=?\)
4.
\(\sum_{k=1}^{10}k=?\)
5.
\(\sum_{k=1}^{7}k^2=?\)
Property 3
\(\sum_{k=1}^{n}a=a+a+\cdots+a=a\cdot n\)
\(\sum_{k=r}^{n}a=a(n-r+1)\)
1.
\(\sum_{k=1}^{10}7=?\)
2.
\(\sum_{k=1}^{20}(-3)=?\)
3.
\(\sum_{k=1}^{15}2=?\)
4.
\(\sum_{k=10}^{20}3=?\)
5.
\(\sum_{k=7}^{23}5=?\)
6.
\(\sum_{k=-8}^{10}4=?\)