माना E, &double;R का एक परिबद्ध (bounded) उपसमुच्चय है। यदि α = glb(E) समुच्चय E का महत्तम निम्नतम बंध (greatest lower bound) है, तो प्रत्येक ε > 0 के लिए, एक ऐसा x ∈ E विद्यमान होगा कि:

Let α, β ∈ (0, &infty;). Consider the infinite series: ∑n ≥ 4 1n(loge n)α (loge(loge n))β Which of the following statements is true?

For a non-negative real number a, let √a denote its non-negative square root. Consider the sequence {xn}n ≥ 1 defined by x1 = 1 and xn+1 = √(1 + xn2n) for n ≥ 1. Which of the following statements is true?