Sequences and Series

Arithmetic sequences

Summation notation (4:26)
1. Writing $1+2+\cdots+10$ using the summation (sigma) notation.
2. Writing $1+2+\cdots+100$ using the summation (sigma) notation.
3. Expanding $\displaystyle\sum_{i=0}^{50}\pi i^2$ .
$\rhd$ Introduction to sequences (8:17) For the sequences $\{1,4,7,10\}$ and $\{3,7,11,15\ldots\}$ , the notation used to indicate a term of the sequence and a formula for it are discussed.
$\rhd$ Introduction to arithmetic sequences (7:06) Recognizing arithmetic sequences, the initial term and their common difference. Explicit and recursive formulas are discussed.
* Practice: Recursive formulas for arithmetic sequences. (4 problems)
* Practice: Extend arithmetic sequences. (4 problems)
* Practice: Explicit formulas for arithmetic sequences. (4 problems)
$\rhd$ Explicit formulas for arithmetic sequences (6:16) Deriving a formula for the sequence $\{-100,-50,0,50, \dots\}$ .

Arithmetic series

$\rhd$ Arithmetic series intro (3:55) The sum of the first $n$ terms in the sequence $\{1,2,3,\dots\}$ .
$\rhd$ Arithmetic series formula (7:46) The sum of the first $n$ terms in the sequence $\{a, a+d, a+2d,\dots\}$ .
$\rhd$ Arithmetic series (sigma notation) (7:01) Find $\displaystyle\sum_{k=1}^{550}(2k+50)$ .
$\rhd$ Arithmetic series (sum expression) (6:46) Find $(-50)+(-44)+(-38)+\dots +2044$ .
$\rhd$ Arithmetic series (recursive formula) (5:20) Given that $a_1=4$ and $a_i=a_{i-1}+11$ , find the sum of the first $650$ terms of the sequence.
* Practice: Arithmetic series. (4 problems)

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The OpenLab at City Tech:A place to learn, work, and share

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