HSE ES Summation Sign

Template:Mergeto Summation Notation

1. Use the summation notation to represent the expression in the first example.

$\sum _1^{100}\frac{1}{n\times (n+1)}$

Change the following into sum notation:

1. $\sum _{n=23}^{1927}n$
2. $\sum _{n=0}^{96}13+3n$
3. $\sum _{n=0}^{99}(4n+1)(-1{)}^{n+1}+(4n+2)(-1{)}^{n+2}+(4n+3)(-1{)}^{n+2}+(4n+4)(-1{)}^{n+1}$
4. $1000-\sum _{n=1}^{\mathrm{\infty }}\frac{-(2n+1)}{\sum _{i=1}^n(2i-1)\times \sum _{j=1}n+2(2j-1)}$

Change the following sum notation into the normal representation:

1. $\begin{array}{ccccc}\pi & =& 4\sum _{k=0}^{\mathrm{\infty }}\frac{(-1{)}^k}{2k+1}& =& 4\frac{(-1{)}^0}{2\times 0+1}+4\frac{(-1{)}^1}{2\times 1+1}+......\end{array}$
2. $\begin{array}{ccccc}\sin x& =& \sum _{k=0}^{\mathrm{\infty }}\frac{(-1{)}^k}{(2k+1)!}{x}^{2k+1}& =& \frac{(-1{)}^0}{(2\times 0+1)!}{x}^{2\times 0+1}+\frac{(-1{)}^1}{(2\times 1+1)!}{x}^{2\times 1+1}+......\end{array}$

Operations of sum notation No exercises yet.

Beyond 1.When n is not 0, factorial can be calculated using this formula:
$n!=\prod _{h=1}^{n}h$