I tried ratio test but what it was giving me didn't feel right and the root one it doesn't seem to be fitting right? It should have more power to the n or it can be good here
#help me with this power series
pliant plank
hexed cypress
I tried ratio test but what it was giving me didn't feel right and the root one ...
Can you show your work for the ratio test? What do you mean it "didn't feel right"?
pliant plank
It should be a limit and in abs value
I know that
It's a sketch
So idk that 4(n+1)^2 ... I can't do anything right?
hexed cypress
It's that... is there an ln in there?
pliant plank
There's two ln ahah
hexed cypress
...okay, can you print it instead of writing in cursive?
hexed cypress
Just to be clear, the summand is (2 - x)^n/(4n^2 + ln(3n^3 + 1)), right?
pliant plank
Better?
pliant plank
Huuuh
hexed cypress
Just to be clear, the summand is `(2 - x)^n/(4n^2 + ln(3n^3 + 1))`, right?
This.
hexed cypress
I've made a discovery.
By the test for divergence, if the series converges at all, it only converges for |2 - x| <= 1.
At least, it only unambiguously converges for that.
Trying to figure out whether it converges outside that range is... a quagmire.
You get into an inf/inf limit situation that L'Hospital's rule only makes worse.
pliant plank
By the test for divergence, *if* the series converges at all, it only converges ...
How did u do it?
hexed cypress
How did u do it?
...lim_(n -> inf) (2 - x)^n/(4n^2 + ln(3n^3 + 1)).
The denominator goes to infinity.
pliant plank
Ye
hexed cypress
The numerator goes to 0 if |2 - x| < 1 and 1 if |2 - x| = 1.
hexed cypress
Well.
pliant plank
You have to check for x changing value
hexed cypress
It goes to 1 if 2 - x = 1 and it's divergent between 1 and -1 if 2 - x = -1.
pliant plank
Right?
hexed cypress
I don't know what that means.
pliant plank
Ahahah