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(1.1) Sigma Notation

Sigma Notation

a) Write the first 5 terms of the sequence with $u_n=2n+1$.
Separate the terms with commas.

A series is a sum of the terms in a sequence.

Examples using sigma notation:

$\displaystyle \sum_{\color{red}{n=1}}^\color{blue}{5} 2n+1=\underset{\color{red}{n=1}}3+\underset{n=2}5+\underset{n=3}7+\underset{n=4}9+\underset{\color{blue}{n=5}}{11}=35$

$\displaystyle \sum_{\color{red}{n=1}}^\color{blue}{4} 2n+1=\underset{\color{red}{n=1}}3+\underset{n=2}5+\underset{n=3}7+\underset{\color{blue}{n=4}}9=24$

$\displaystyle \sum_{\color{red}{n=3}}^\color{blue}{5} 2n+1=\underset{\color{red}{n=3}}7+\underset{n=4}9+\underset{\color{blue}{n=5}}{11}=27$

For each of the following series in sigma notation, write the terms as a sum.
For example:
$\displaystyle \sum_{n=2}^5 2n+1=5+7+9+11$

a) $\displaystyle \sum_{n=1}^3 2n+1=$

b) $\displaystyle \sum_{n=3}^6 2n+1=$

c) $\displaystyle \sum_{n=1}^4 7n-4=$

d) $\displaystyle \sum_{n=1}^5 -3n+8=$

e) $\displaystyle \sum_{n=1}^5 1-\frac{2}{7}n=$
*Write each term as a fraction

f) $\displaystyle \sum_{n=1}^4 2^n=$

g) $\displaystyle \sum_{n=1}^5 (-3)^{n-1}=$

h) $\displaystyle \sum_{n=3}^8 64\left(\frac{1}{2}\right)^{n-1}=$

i) $\displaystyle \sum_{n=2}^6 -n\left(n-1\right)=$

Use your calculator to calculate the following sums.
On the TI-Nspire CX, press alt-text then alt-text

a) $\displaystyle \sum_{n=1}^{50} 2n+1=$

b) $\displaystyle \sum_{n=1}^{100} n=$

c) $\displaystyle \sum_{n=1}^{24} 1-\frac{2}{3}n=$

d) $\displaystyle \sum_{n=1}^{15} (-3)^{n-1}=$