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Let us test the series: 1 - 1/2 + 1/3 - 1/4 + 1/5 - ... Step 1: Identify the parts. Our series is alternating. The numbers (ignoring the signs) are 1, 1/2, 1/3, 1/4, 1/5. Let's call the value without the sign 'a'. So, a(n) = 1/n. Step 2: Check if numbers are shrinking. Is 1/2 smaller than 1? Yes. Is 1/3 smaller than 1/2? Yes. As n gets bigger, 1/n always gets smaller. Rule 1 passed. Step 3: Check if the limit reaches zero. As n becomes a huge number (like a million), what happens to 1/n? 1/1,000,000 is almost zero. Rule 2 passed. Conclusion: Since both rules are true, this alternating series converges!