Question

Help Please!

Answer 1

For #2, I understand why the intervals are -1 and 1. But why is one closed brackets, while the other one is open?

Answer 2

@zepdrix @mathmate

Answer 3

from my understand Bracket means included and parenthese means excluded

Answer 4

I dont understand why though. When i find the power series. I get \[|x| = 1 \rightarrow x = -1, 1\]

Answer 5

@Directrix @sweetburger

Answer 6

for the negative -1 u will get cancellations across the sum

Answer 7

so it converges at -1 too

Answer 8

where as for 1, ur back to the harmonic series case and its not converging

Answer 9

u can look at it as a telescoping sum

Answer 10

-1/9 + 1/18 -1/27 + 1/36....

Answer 11

does that converge or diverge

Answer 12

by alternating series test it converges

Answer 13

http://tutorial.math.lamar.edu/Classes/CalcII/AlternatingSeries.aspx

Answer 14

its an intuitive way to understand the proof, and then u can try to prove it

Answer 15

like u subtracted more than u added to begin with if u look at the 2 numbers.. and then the 2nd 2 numbers uve added more than u just subtracted... and this keeps going on and the numbers this keeps happening to is decreasing

Answer 16

so u must converge

Answer 17

To me, it is just put -1 and 1 into the series
with -1, you have \(\dfrac{(-1)^n}{9n-1}\) converge by the proof

with 1, you have \(\dfrac{1}{9n-1}\) divergence.

Hence you take the value which makes the series convergence.

[-1,1)