Question

Given the sequence in the table below, determine the sigma notation of the sum for term 4 through term 15.

Answer 1

is my answer correct

Answer 2

Yep

Answer 3

Correct

Answer 4

what about this one @Lord_Box

Answer 5

Not quite correct

Answer 6

can you explain

Answer 7

do i just add all of the sums plugging in 1 through 7?

Answer 8

Yes

Answer 9

\[2 - 4 + 8...\]

Answer 10

Or you can use the geometric sum formula
\[\large\rm Sum=\frac{a(1-r^n)}{1-r} \]

Answer 11

86?

Answer 12

yes

Answer 13

what is a and r

Answer 14

and n

Answer 15

a is the initial term, which was 2. r is the common ratio, (-2), n is the number of times, which was 7.

Answer 16

i don't know what this is

Answer 17

It's a geometric series

Answer 18

how do i solve

Answer 19

First identify if its convergent or divergent

Answer 20

how do i do that

Answer 21

There is a sort of formula.

http://study.com/cimages/multimages/16/arithmetic-geometric-series-formulas.jpg

Answer 22

You have to look at the number inside of the parentheeses and look to see if it is greater or less than one

Answer 23

so convergent?

Answer 24

still confused I'm sorry

Answer 25

Can you find out the limit of the above expression?

Answer 26

infinity??

Answer 27

\[\large\rm \lim_{x\rightarrow\infty} {\frac{5^x}{6^x}}\]

Answer 28

5/6?

Answer 29

And according to albert test, it says that if the limit is smaller than 1, then the series converges. So is the series convergent or divergent?

Answer 30

convergent

Answer 31

so then the sum?

Answer 32

Use the geometric formula above

Answer 33

what formula

Answer 34

@FaiqRaees

Answer 35

Or you can use the geometric sum formula
\[\large\rm Sum=\frac{a(1-r^n)}{1-r}\]

Answer 36

so what is a r and n

Answer 37

a=8
n= (any big value like 100)
r=5/6

Answer 38

so 48?

Answer 39

also is this correct?

Answer 40

@FaiqRaees

Answer 41

@Lord_Box

Answer 42

It is convergent, but the sum is wrong. See the first term is 1200 so how could the sum be less than first term?

Answer 43

Try plugging in 1 to both of the convergent series.

Answer 44

is it c?

Answer 45

Yep

Answer 46

yep