Question

I need help in Series Question.
The series is : (1/2) + (2/3)x + (3/4)^2x^2 + (4/5)^3x^3
this is test for convergence

Answer 1

you prolly need to define a rule for the sequence of coefficients

Answer 2

\[\sum_{n=0}^{\infty}~\frac{n+1}{n+2}x^n\]
seems apropriate to play with

Answer 3

might be reading some of it wring tho

Answer 4

\[\frac12+\sum_{n=1}^{\infty}~\frac{(n+1)^n}{(n+2)^n}x^n\]
might be better

Answer 5

\[\lim\frac{(n+1+1)^{n+1}x^{n+1}}{(n+1+2)^{n+1}}\frac{(n+2)^n}{(n+1)^nx^{n}}\]
\[|x|\lim\frac{(n+2)^{2n+1}}{(n+3)^{n+1}(n+1)^n}\]
might be able to determine of the rational expression is a higher degree top to bottom

Answer 6

as n gets large this simplifies to:\[\frac{n^{2n+1}}{n^{n+1}*n^n}\to1\]
if i see it right

Answer 7

yes and thats where the problem lies... it goes to 1.. when i apply root test x>1 its divergent. x<1 its convergent but what should I do when x=1??

Answer 8

the coeffs go to 1, not the limit of the function

Answer 9

|x| < 1, when -1 < x < 1

this is the interval of convergence

Answer 10

when x >= 1, you either have to try a different appraoch or just be sated that its divergent ....

Answer 11

ok thanx

Answer 12

good luck

Answer 13

i just joined how to give u medals or whatever for your effort in helping??

Answer 14

there should be a "best respose" button to the right of all my posts. if not, hit refresh. but a simple thank you is worth more to me than some fictitious award :)

Answer 15

done both :D

Answer 16

again, good luck ;)