Discussion
The integral \( \displaystyle\int_{1}^{\infty} \frac{dx}{x^{p}} \) converges precisely when
Answer: B
For \( p \neq 1 \) the antiderivative is \( x^{1-p}/(1-p) \), which stays finite as \( x \to \infty \) only when \( 1 - p < 0 \). At \( p = 1 \) the antiderivative is \( \ln x \), which diverges. So the boundary case itself fails, and the condition is strict: \( p > 1 \)
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