A function f : &DoubleStruckCAPITALR; → &DoubleStruckCAPITALR; is defined by f(x) = 2x when x ∈ &DoubleStruckCAPITALQ;, and f(x) = 1 - x when x ∈ &DoubleStruckCAPITALR;\&DoubleStruckCAPITALQ;. Then:

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?