Question

Find the sum of the following infinite geometric series, if it exists.
one-third plus one-ninth plus one-twenty-seventh + one-eighty-first plus and so on

Answer 1

Find the sum of the following infinite geometric series, if it exists.
4 + 3.2 + 2.56 + 2.048 + …

Answer 2

don't use decimals:)
1/3+1/9+1/27....take the second divided by the first term
what do you get?

Answer 3

wait, is this two questions?

Answer 4

no

Answer 5

how does 4 + 3.2 + 2.56 + 2.048 + relate to 1/3+1/9...?

Answer 6

sorry those are two different questions

Answer 7

1/9)/1/3 = 1/3
so your ratio is 1/3
first term is 1/3
so
\[\frac{\frac{1}{3}}{1-\frac{1}{3}}\]

Answer 8

so 1/3 is the answer

Answer 9

We observe that the common ratio is the ratio of the successive and the previous term:\[\bf Common \ ratio=\frac{ \frac{ 1 }{ 9 } }{ \frac{ 1 }{ 3 } }=\frac{ \frac{ 1 }{ 27 } }{ \frac{ 1 }{ 9 } }=\frac{ 1 }{ 3 }\]So the geometric series is given by ('a' is the first term; 'r' is the common ratio):\[\bf ar^{n-1}=\frac{ 1 }{ 3 }\left( \frac{ 1 }{ 3 } \right)^{n-1}\]We observe that the series is convergent, i.e. \(\bf |r|<1\), so the sum of the series will be given by:\[\bf S_n=\frac{a}{1-r}\]Can you evaluate the sum?

@dedog55

Answer 10

\[\frac{\frac{1}{3}}{1-\frac{1}{3}}=\frac{\frac{1}{3}}{\frac{2}{3}}=\frac{1}{3}*\frac{3}{2}=\frac{1}{2}\]

Answer 11

Find the sum of the following infinite geometric series, if it exists.
4 + 3.2 + 2.56 + 2.048 + …

Answer 12

what is the ratio?

Answer 13

I don't know how to do do this

Answer 14

yes you do.

Answer 15

divide the second term by the first

Answer 16

that is your ratio...

Answer 17

what is the ratio?

Answer 18

1.25

Answer 19

3.2/4 = 1.25??????

Answer 20

ya

Answer 21

nope...the top is smaller than the bottom so its less than one

Answer 22

no its .8

Answer 23

yes

Answer 24

ok so what is the first term?

Answer 25

4

Answer 26

\[\frac{firstterm}{1-ratio}=answer\]

Answer 27

is it 3.2

Answer 28

\[\frac{4}{1-0.8}=\frac{4}{0.2}=?\]

Answer 29

how did you get 3.2?

Answer 30

I did it wrong

Answer 31

its 20 hahaha

Answer 32

What is the r value of the following geometric sequence?
40, 20, 10, 5,…

Answer 33

so what part of divide the second term by the first are you not getting?

Answer 34

and....we already went over this problem:)

Answer 35

sorry not trying to be mean, but you ask the same question over and over with different numbers:) so lets get to why :)

Answer 36

sorry I sent you the wrong problem

Answer 37

Find two geometric means between 5 and 135.

Answer 38

you should close this and open another.