Went to my exam and looked at my test, saw a function hadn't seen before.
Not just a bunch of powers of x, polynomials don't scare me no more.
Well it was like that but it went on much longer,
Techniques I use better be a lot stronger.
This problem feels so urgent!
How do I know when this thing's convergent?
Really nervous, and I've got a lot of queries,
How to deal with this damn power series?
But then I knew to find the radius
Of convergence for the sum
Of convergence for the sum
Of convergence for the sum!
Chorus:
So I threw my hands up, I got this one solved,
Ratio test saves the day!
Dividing by terms like "Yeah!"
Takin' my limits like "Yeah!"
Got my hands up, I got this one solved,
I know I'm gonna be okay.
Yeaaaaaaah, bound the value of x-a.
Yeaaaaaaah, bound the value of x-a.
Inside the sum, if this is sufficient, got (x-a) to the n.
Left of that is a coefficient, and now I pick up my pen.
In the denominator, I'm gonna write that product,
Numerator's almost got all the same stuff,
Except this one part's such fun:
To all of the n's I add a plus one.
Almost done! I think "Good job! Now gal you
know you gotta take the absolute value!"
Then I know I check the limit
As n goes on and on
As n goes on and on
As n goes on and on
(Chorus)
Set that limit less than one (less than one)
Oh my word we're almost done (almost done)
Solve that for (x-a) (minus a)
The radius shows up as plain as day!
(Chorus x2)