Question

Express the series below in summation notation for the specified number of terms.
i)2 + 4 + 8 + 16

Answer 1

@secretslocked what is being added each term?

Answer 2

any idea?

Answer 3

hint: a number to some power

Answer 4

@billj5
there is no power.

Answer 5

2^1 + 2^2 + 2^3 + 2^4

Answer 6

@billj5
^what is that for?

Answer 7

that looks like the series right?

Answer 8

2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16

Answer 9

summation n=1 to 4 of ????

Answer 10

@billj5
the question doesn't say it just gave me
i)2 + 4 + 8 + 16 and with 2 more as well

Answer 11

what are the next 2?

Answer 12

b. 10 + 14 + 18 + 22

Answer 13

lol i thought you meant two more terms

Answer 14

so can you do any of those problems?

Answer 15

i think so,currently am trying

Answer 16

not sure of my answers though

Answer 17

can you draw what you have for one of your answers?

Answer 18

10^4+10^8+10^2

Answer 19

^ for b)

Answer 20

no thats not right

Answer 21

first off do you understand what a series is, and what summation notation is?

Answer 22

no.

Answer 23

do you want to know?

Answer 24

yes.

Answer 25

ok so first i will tell you what a sequence is

Answer 26

ok

Answer 27

would you rather watch a video?

Answer 28

it's all blocked(visiting family in pk)

Answer 29

ok, so a sequence is a list of numbers, thats it, so like 1, 2, 3, 4 is a sequence, 1, 3, 5, 7, is a sequence.. etc, got that?

Answer 30

yup.

Answer 31

ok im not going to worry about infinite sequences right now because your question doesnt ask that, but just know, that those numbers could keep going, 1,2,3,4,... the dots mean the numbers that come after, like 5,6,7,8,... etc

Answer 32

ok so a "series" is just a sequence of numbers, where you sum all of the numbers in the sequence, so instead of 1,2,3,4 you have 1+2+3+4, ok?

Answer 33

okayy.

Answer 34

ok so now you know what a series is, one way to represent a series is with summation notation, it uses a greek letter sigma, so you know what sigma looks like, can you draw it?

Answer 35

@secretslocked do you know what sigma looks like?

Answer 36

yes;

Answer 37

upper case sigma

Answer 38

ok draw it

Answer 39

click draw button

Answer 40

ok so that think that looks like an E, is sigma

Answer 41

ok

Answer 42

ok, from that picture, do you know what the n=2 means?

Answer 43

no.

Answer 44

ok, n is a variable, and you are assigning the value of 2 to it, you understand that part?

Answer 45

so n is any number and 2 is the value?

Answer 46

well the point of a variable is that n can change, so for now n=2 but it can be other values.. is that what you mean?

Answer 47

28 + 2i

Answer 48

yes.

Answer 49

ignore what @OpiGeode said, it means nothing

Answer 50

Rude.

Answer 51

okay.

Answer 52

ok so when they write n=2 underneath that means that is the starting value of n in the summation, you are starting where n=2

Answer 53

@OpiGeode no its rude to interrupt this learning process, to give an incorrect direct answer

Answer 54

see the 5 on top of sigma? what do you think that means?

Answer 55

Well sorry if my answer was incorrect.

Answer 56

@secretslocked what do you think the 5 means?

Answer 57

i don't know-

Answer 58

the 5 is the value of n in which the series ends

Answer 59

now the important part is that n increases by one for each term

Answer 60

wait the 2 is on top of the n

Answer 61

im only talking about the part on the left side, the sigma part

Answer 62

oh 5 is end point of the series, and two is the starting point?

Answer 63

oh

Answer 64

yes,

Answer 65

ok so for the first term n=2, and the last term, n=5 make sense?

Answer 66

yes

Answer 67

ok so now the right hand side, where you see n^2, that tells you what the current term will be

Answer 68

so can you tell me what the first term in the series is?

Answer 69

2

Answer 70

im talking about the one in the picture

Answer 71

right?

Answer 72

remember we are starting at n=2

Answer 73

same here,

Answer 74

3?

Answer 75

so if n=2 you would replace the n with 2 , so instead of n^2 you have 2^2,

Answer 76

does that make sense?

Answer 77

maybe-it starts like that right then 3 ,4 and 5-because it's the end of the series?

Answer 78

ok but take it one step at a time

Answer 79

or is it the other way round like;

Answer 80

let me draw it, much easier than explaining

Answer 81

in words

Answer 82

2(2)+2(3)+2(4)+2(5)

Answer 83

thats close but no let me draw

Answer 84

u have the right idea almost, just a little bit off

Answer 85

ok.

Answer 86

do you understand what 2^2 means?

Answer 87

@secretslocked

Answer 88

2 square?

Answer 89

what does it equal?

Answer 90

4

Answer 91

ok what does 2^3 equal?

Answer 92

6

Answer 93

no

Answer 94

8