[Verse 1] When infinity calls your name And series stretch beyond the frame We need some tests to find the truth Does it settle or break loose? Compare your terms to something known If zero's trapped between the zones And B converges, A will too Comparison will see you through [Chorus] Ratio, root, and integral ways P-series counting down the days When alternating signs appear Convergence tests make patterns clear Less than one means settle down Greater than one will crash the ground Choose your weapon, make the call Infinity won't fool us all [Verse 2] Take the limit of A-next over A-now If it's less than one, take a bow Greater than one spells disaster Ratio test reveals the master Root test pulls the nth power out Same rules apply without a doubt For exponentials climbing high These tests will separate the sky [Chorus] Ratio, root, and integral ways P-series counting down the days When alternating signs appear Convergence tests make patterns clear Less than one means settle down Greater than one will crash the ground Choose your weapon, make the call Infinity won't fool us all [Bridge] Harmonic series tricks the mind One over N seems so refined But it diverges, growing free The boundary's where P equals three... no, one! Alternating saves the day When magnitudes decay away Decreasing down to zero's shore Convergence knocks upon the door [Verse 3] Integral test builds the bridge Between the sum and calculus ridge If function falls and stays above The series dance the same old love P-series holds the golden key When P's greater than one, we're free But harmonic at P equals one Diverges when the race is run [Final Chorus] Ratio, root, and integral ways P-series counting down the days When alternating signs appear Convergence tests make patterns clear Fast enough to zero's call Or infinity claims it all Master these and you'll decode Every series on the road
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