Part BCSIR NET June 2025log-x-turns-the-interval-into-0-to-2pi-so-the-eigenvalues-are-n-squared-over-4

Log x turns the interval into 0 to 2pi so the eigenvalues are n squared over 4

Let $(λ_{n})_{n} \in N$ be the sequence of eigenvalues of the Sturm-Liouville problem (d/dx)(x dy/dx $) + (λ / x) y = 0, 1 < x <$ $e^{2 π}$ , y(1) = 0, $y (e^{2 π})$ = 0. Then $\sum_{n}$ ₌ $_{1}^{\infty} 1/ λ_{n}$ is equal to

A. $π^{2} /12$
B. $2 π^{2} /3$ ✓
C. $π^{2} /4$
D. $π^{2} /16$

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests execution slip.

See pricing

50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

Related counterexample: Every boundary value problem has a Green's function

Log x turns the interval into 0 to 2pi so the eigenvalues are n squared over 4

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