stuffs

0.0(0)
Studied by 1 person
linked notesView linked note
call kaiCall Kai
learnLearn
examPractice Test
spaced repetitionSpaced Repetition
heart puzzleMatch
flashcardsFlashcards
GameKnowt Play
Card Sorting

1/7

encourage image

There's no tags or description

Looks like no tags are added yet.

Last updated 1:09 AM on 6/20/24
Name
Mastery
Learn
Test
Matching
Spaced
Call with Kai

No analytics yet

Send a link to your students to track their progress

8 Terms

1
New cards

Define Geometric Series. How do you calculate it? What is a restriction on the equations?

the sum of the terms in a geometric sequence

  • S = sum

  • u1 = 1st term

  • r = common ratio

  • n = # of terms

r ≠ 1

<p><span>the sum of the terms in a geometric sequence</span></p><ul><li><p><span>S = sum</span></p></li><li><p>u<sub>1</sub> = 1<sup>st</sup> term</p></li><li><p>r = common ratio</p></li><li><p>n = # of terms</p></li></ul><p><strong><span style="color: red">r ≠ 1</span></strong></p>
2
New cards

What does it mean if a series is Divergent or Convergent?

Series become divergent if the sum approaches infinity as n approaches infinity.

Series become convergent if the sum approaches a limit as n approaches infinity.

3
New cards

If |r| < 1 , then the series is … Why is this so?

convergent since as r gets powered, r gets infinity smaller, leading to 0.

e.g.

1: ½

2: ½×½=¼ see how it gets smaller

<p><strong><span style="color: red">convergent</span></strong> since as r gets powered, r gets infinity smaller, leading to 0.</p><p>e.g. </p><p>1: ½</p><p>2: ½×½=¼ see how it gets smaller</p>
4
New cards

Proofs

knowt flashcard image
5
New cards

/eaWhat is the notation for Pascal’s Triangle? How can we find any term we want?

Notation: tn,r

  • n = row

  • r = position

<p>Notation: tn,r</p><ul><li><p>n = row</p></li><li><p>r = position</p></li></ul>
6
New cards

Define Combination and Permutation

Combination: the selection from a set (group of items) without regard to order.

Permutation: the selection from a set (group of items) with regard to order.

<p><strong><span style="color: red">Combination</span></strong>: <span>the selection from a set (group of items) </span><strong><span><mark data-color="red">without</mark></span></strong><span> regard to order.</span></p><p><strong><span style="color: purple">Permutation</span></strong>: the selection from a set (group of items) <strong><mark data-color="purple">with</mark></strong> regard to order.</p>
7
New cards
<h3 collapsed="false" seolevelmigrated="true">What does each component represent?</h3>

What does each component represent?

n = total # of available things

r = chosen # of available things

<p>n = total # of available things</p><p>r = chosen # of available things</p>
8
New cards

What is the Binomial Theorem?

knowt flashcard image