Question

find the sum

Answer 1

\[\sum_{n=1}^{\infty} \frac{ 1+4^n }{ 8^n }\]

Answer 2

did you check the convergence

Answer 3

how is the sum performed here? is it used with \[\frac{ a }{ 1-r }\]

Answer 4

it converges yes

Answer 5

hmm i' thinking of doing a separation
\[\frac{1+4^n}{8^n}=(\frac{1}{8})^n+(\frac{1}{2})^n\]

Answer 6

yes, and that is what i did to find convergence... how do we proceed with finding the sum?

Answer 7

hmm there should the summation of (1/2)^n from 1 to k

Answer 8

it is like you mentioned above just check your notes how to do it

Answer 9

i honestly forgot how to do it

Answer 10

thanks anyway

Answer 11

http://en.wikipedia.org/wiki/1/2_%2B_1/4_%2B_1/8_%2B_1/16_%2B_%E2%8B%AF
this the summation

Answer 12

as i said they used what you said above

Answer 13

do i do this separately? r= 1/2 and then again r= 1/8? and then add those two together?

Answer 14

the other some i'm thinking of \[(\frac{1}{2})^{3n}\]

Answer 15

yes of course!

Answer 16

each one separately

Answer 17

sum not some* typo

Answer 18

\[\frac{ \frac{ 1 }{ 2 } }{ 1-\frac{ 1 }{ 2 } }+ \frac{ \frac{ 1 }{ 8 } }{ 1-\frac{ 1 }{ 8 } }\]

Answer 19

they are really the same after looking from a different angle
they are given the same result

Answer 20

no my friend

Answer 21

look what i did 1/8 can be written as (1/2)^3
so we get ((1/2)^n)^3

Answer 22

so it is really the same sum raised to the power 3

Answer 23

the sum would be 2
1+1^3=1+1=2

Answer 24

it says the answer is 8/7... but it does not show me how they got that.... so i know 2 is not correct

Answer 25

if you did it the other way you get 8/7

Answer 26

the way you suggested

Answer 27

\[\frac{ \frac{ 1 }{ 8 } }{ \frac{ 8 }{ 8 }-\frac{ 1 }{ 8 } }= \frac{ 1 }{ 8 }(\frac{ 7 }{ 8 })= \frac{ 7 }{ 64 }\]

Answer 28

i did that backwards

Answer 29

hmm that is incorret
should 8/7 (1/8)

Answer 30

you have to flip the fraction

Answer 31

\[\frac{ 1 }{ 8 }(\frac{ 8 }{ 7 })= \frac{ 8 }{ 56 }\]

Answer 32

lol oops

Answer 33

you should have 1/7 +1 =8/7

Answer 34

which is what you are looking for

Answer 35

yep. thamks!

Answer 36

thanks

Answer 37

no problem

Answer 38

i always need to "see" it,..i donno y

Answer 39

I'm wondering why the other way i did went off the loop
it should work!! something has to do with infinity i guess

Answer 40

it sounded so "nice" too! it is because 1/2 became just 1 when we applied it to the sum formula.... and 1 to the power of anything is just 1

Answer 41

thanks for being a trooper with me through this

Answer 42

it is the problem of infinity for sure
1^oo is somewhat problematic

Answer 43

true!

Answer 44

oh well you solved anyway :)

Answer 45

yep and im sure ill be back on with another

Answer 46

hehe feel free :)