Question

calc-geometric series-how to solve for x?

Answer 1

\[\sum_{n=1}^{\infty} 7x ^{9n}=42\]

Answer 2

i would divide by 7 first

Answer 3

since \[\sum_{n=1}^{\infty} 7x ^{9n}=42\] is the same as \[7\sum_{n=1}^{\infty} x ^{9n}=42\]

Answer 4

after that, it is a well known geometric series right?

Answer 5

\(x^{9n}=y^n\), for what \(y\)?

Answer 6

\[\sum_{n=1}^{\infty}ar^n=\frac{a}{1-r}\]in your case both \(a\) and \(r\) are \(x^{9n}\)

Answer 7

\[=\frac{ x ^{9n} }{ 1-x ^{9n} }\]

Answer 8

yes

Answer 9

i mean no

Answer 10

i made a typo above
should have said "in your case \(r\) and \(a\) are both \(x^9\)

Answer 11

\[=\frac{ x^9 }{ 1-x^9 }\]

Answer 12

right
set that equal to \(6\) solve for \(x^9\) then i guess write the ninth root of the result

Answer 13

another oddball question from whatever system you are using

Answer 14

let me know when you get it

Answer 15

i got it, 0.983

Answer 16

idk seems reasonable
i solved \[\frac{x}{1-x}=6\]got \[x=\frac{6}{7}\] but i'll be damned if i know what the ninth root of that number is

Answer 17

yeah calculator gave me the same thing

Answer 18

thank you