Question

Power series convergence

Answer 1

I is clearly wrong - recall the fact that harmonic series diverges but the alternating harmonic series converges

Answer 2

that eliminates first and third options

Answer 3

Ok

Answer 4

II is trivially true because -2 lies in the interval |x|<3

Answer 5

But, I thohught we only test abs(x)<1

Answer 6

the power series converges for x=3, and it is centered at 0, so the interval of convergence includes (-3, 3]

Answer 7

III looks wrong since \[\Large -1<x <1\]
\[\Large -3<x<-1\]

Answer 8

III is also correct actually, shifting the center wil have no effect on radius of convergence

Answer 9

|x-2|<1

gives you

1<x<3

Answer 10

Oh, ok

Answer 11

Oh, how come I can't do what I did up there

-1<x<1
-3<x-2<-1 (I forgot the x-2)

Aren't I taking 2 from both sides?

Answer 12

thats an interesting question @doulikepiecauseidont

Answer 13

I'll try and answer this after sometime, need to think a bit...
@dan815 @Kainui @TuringTest