Sigma Notation
Write the first 6 terms of the sequence with $u_n=2n+1$.
Separate the terms with commas.
Separate the terms with commas.
A series is a sum of the terms in a sequence.
Examples using sigma notation:
$\displaystyle \sum_{\textcolor{red}{n=1}}^\textcolor{blue}{6} 2n+1=$
$\underset{\textcolor{red}{n=1}}3+\underset{n=2}5+\underset{n=3}7+\underset{n=4}9+\underset{{n=5}}{11}+\underset{\textcolor{blue}{n=6}}{13}$
$\displaystyle \sum_{\textcolor{red}{n=1}}^\textcolor{blue}{4} 2n+1=$
$\underset{\textcolor{red}{n=1}}3+\underset{n=2}5+\underset{n=3}7+\underset{\textcolor{blue}{n=4}}9$
$\displaystyle \sum_{\textcolor{red}{n=3}}^\textcolor{blue}{5} 2n+1=$
$\underset{\textcolor{red}{n=3}}7+\underset{n=4}9+\underset{\textcolor{blue}{n=5}}{11}$
For each of the following series in sigma notation, write the terms as a sum.
For example:
$\displaystyle \sum_{n=2}^5 2n+1=$
$5+7+9+11$
$\displaystyle \sum_{n=1}^3 2n+1=$
$\displaystyle \sum_{n=3}^6 2n+1=$
$\displaystyle \sum_{n=1}^4 7n-4=$
$\displaystyle \sum_{n=1}^5 -3n+8=$
$\displaystyle \sum_{n=1}^5 1-\frac{2}{7}n=$
*Write each term as a fraction
*Write each term as a fraction
$\displaystyle \sum_{n=1}^4 2^n=$
$\displaystyle \sum_{n=1}^5 (-3)^{n-1}=$
$\displaystyle \sum_{n=3}^8 64\left(\frac{1}{2}\right)^{n-1}=$
$\displaystyle \sum_{n=2}^6 -n\left(n-1\right)=$
Use your calculator to calculate the following sums.
On the TI-Nspire CX, press 
then 
$\displaystyle \sum_{n=1}^{50} 2n+1=$
$\displaystyle \sum_{n=1}^{100} n=$
$\displaystyle \sum_{n=1}^{24} 1-\frac{2}{3}n=$
$\displaystyle \sum_{n=1}^{15} (-3)^{n-1}=$
Express the following series using sigma notation.
$6+9+12+15+18+21+24$
$\displaystyle \sum_{n=1}^{7}$
$6-12+24-48+96$
Give your answer in the form $a\left(b\right)^{n-1}$
Give your answer in the form $a\left(b\right)^{n-1}$
$\displaystyle \sum_{n=1}^{5}$
$1+4+9+16+25+36+49+64+81+100$
$\displaystyle \sum_{n=1}^{10}$
$\displaystyle 1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\cdots $
Give your answer in the form $a\left(b\right)^{n-1}$
Give your answer in the form $a\left(b\right)^{n-1}$
$\displaystyle \sum_{n=1}^{\infty}$
Exercises
(Core 5F on P.113) #3ad, 4ef, 5 (use your GDC for all questions)