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Using the Integral Test for infinite series and the Comparison Test for integrals (Theorem \ref{thm 8.7.2}), determine whether each of the following series converges or diverges.

• [math]\sum_{k=1}^\infty e^{-k^2}[/math]
• [math]\sum_{i=1}^\infty \frac1{i^2} \sin \frac1{i^2}[/math].