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Nothing quite captures the existential dread of a Real Analysis exam like staring at an infinite series and being asked to determine if it converges. The series shown here—with that delightful n³ in the denominator and sin²(n) in there just to spice things up—is the kind of problem that makes you question every life choice that led you to this moment.
You start off confident, thinking "okay, I'll try the ratio test... wait, maybe comparison test? Or integral test?" Two hours later, you've filled three pages with attempted proofs, consulted every convergence test known to humanity, and you're no closer to an answer. The sin²(n) oscillates between 0 and 1, but not in any helpful periodic way since n is an integer—it's just chaos dressed up in mathematical notation.
By the end of the exam, you've achieved a state of mathematical enlightenment where you realize this problem was specifically designed by your professor to humble you. Somewhere, Cauchy is laughing.
