Question

radius of convergence

Answer 1

\[\sum_{n=0}^{\infty}(x-2)^n/10^n\]

Answer 2

heyy help

Answer 3

i am confused about this radius

Answer 4

when the radius is infinite

Answer 5

radius of convergence is the value of x upto which the above series is convergent {i.e. Following values of the series are smaller than the initial values }

Answer 6

8

Answer 7

book says 10

Answer 8

any series is convergent if the term yields <1 value ..
hence (x-2)/10<1 ; X<12 hence 12 is radius of convergence

Answer 9

you want:
\[\left| \frac{x-2}{10} \right|< 1\]

Answer 10

yes joe

Answer 11

soory calc mistake

Answer 12

do u find 10 phaniraj?

Answer 13

so you get:
\[\left| \frac{x-2}{10} \right|<1 \Rightarrow -1< \frac{x-2}{10} < 1 \Rightarrow -10<x-2<10\]\[-8<x<12\]

Answer 14

so x can be inbetween -8 and 12, giving an interval radius of 10. (the whole interval is 20 units long)

Answer 15

joe i got nowww ,oh thanks