Question

radius of convergence:

2x^(2n)/n+1

Answer 1

\[\sum_{n=1}^{\infty} 2x ^{2n}/(n+1)\]

Answer 2

using the ratio test

Answer 3

\[2x ^{2(n+1)}/((n+1)+1) \times (n+1)/(2x ^{2n})\]

Answer 4

i am going to guess (-1,1)

Answer 5

hmm... but i have a problem with the next step

Answer 6

wait guys..

Answer 7

That's the interval of convergence. The radius of convergence would be 1 in that case.

Answer 8

yes true

Answer 9

this one the first fraction \[2x ^{2n+2}/n+2\]

Answer 10

yes so compute
\[\frac{x^{2n+2}}{n+2}\times \frac{n+1}{x^{2n}}\]

Answer 11

how can i rewrite this:

like?

\[2x ^{2n} * 4x ^{2} / (n+2)\]

or like

\[2x ^{2n} * 2x ^{2}\]

Answer 12

how do you insert the fraction with the equation?

Answer 13

the ratio is the one i wrote. it is literally
\[\frac{a_{n+1}}{an}\] but for practical purposes you almost always have a ratio to begin with so you multiply by the reciprocal as you would normally

Answer 14

\frac{a}{b}

Answer 15

\[\frac{2x ^{2n}4x ^{2}}{n+2} \times \frac{n+1}{2x ^{2n}}\]

or

\[\frac{2x ^{2n}2x ^{2}}{n+2} \times \frac{n+1}{2x ^{2n}}\]

Answer 16

im confussed with the \[4x^{2}\] and \[2x^{2}\]

Answer 17

ignore the 2 take it right out front of the sum. it is a red herring

Answer 18

or just cancel at that step

Answer 19

huh?

Answer 20

if i cancel that step i dont know how to go further

Answer 21

ii think that 4 is a mistake

Answer 22

replace n by n + 1 in your expression. it does not effect the "2"

Answer 23

could you write out what you are saying?

Answer 24

i dont understand it anymore..

Answer 25

1 thing i know is that the 2x^2n term dissapears

Answer 26

yes ok
\[a_n=\frac{2x^{2n}}{n+1}\]
\[a_{n+1}=\frac{2x^{2(n+1)}}{n+1+1}=\frac{2x^{n+2}}{n+2}\]

Answer 27

so there is no 4 in it. increase n by 1 is all your ratio is therefore
\[\frac{2x^{2n+2}}{n+2}\times \frac{n+1}{2x^{2n}}\]
\[=\frac{x^2(n+1)}{n+2}\]

Answer 28

but isnt \[2x ^{2n+2} = 2x ^{2n}*2n ^{2}?\]

Answer 29

oops forgot the x

Answer 30

the n is a x

Answer 31

owh wait i got it... the 2 is just a scalar :) nvm ^^ thank youu <3

Answer 32

yw,
and yes, the 2 you could safely ignore