मान लीजिए कि अंतराल [0,1] पर g(x) इस प्रकार परिभाषित है कि यदि x परिमेय है तो g(x) = x, और यदि x अपरिमेय है तो g(x) = 0। निम्नलिखित में से कौन सा कथन सत्य है?

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?