A sequence of numbers t_{1}, t_{2}, t_{3}, \ldots has its terms defined by t_{n}=\frac{1}{n}-\frac{1}{n+2} for every integer n \geq 1. For example, t_{4}=\frac{1}{4}-\frac{1}{6}. What is the largest positive integer k for which the sum of the first k terms (that is, t_{1}+t_{2}+\cdots+t_{k-1}+t_{k} ) is less than 1.499?
Answer Choices
A. 2000
B. 1999
C. 2002
D. 2001
E. 1998