Word Count : 345

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समुच्चय \( S = \left\{ \frac{1}{n} + \frac{1 + (-1)^n}{3} : n \in \mathbb{N} \right\} \) को विवृत नहीं होने के रूप में दिखाने के लिए, हम यह दिखाएंगे कि इस समुच्चय में अनंत संख्या में अलग-अलग मान होते हैं, अर्थात समुच्चय में कोई सीमा नहीं है। समुच्चय \( S \) के प्रत्येक तत्व का रूप है: \[ a_n = \frac{1}{n} + \frac{1 + (-1)^n}{3} \] यहाँ, \( (-1)^n \) के दो संभावित मान होते हैं: 1. यदि \( n \) सम है, तो \( (-1)^n _____ ________ _____ _____ ________ __________ _________ __________.
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