Explanation

Note: the stem's radicals are garbled; it is the classic sum √(1+1/1²+1/2²)+…+√(1+1/2007²+1/2008²). Each term satisfies √(1+1/n²+1/(n+1)²) = 1+1/n−1/(n+1). Summing for n = 1…2007 telescopes to 2007 + 1 − 1/2008 = 2008−1/2008 (option A).