$\large\frac{1}{1.3}+\frac{1}{2.5}+\frac{1}{3.7}+\frac{1}{4.9}+....=$

Question

\[\begin {array} {1 1} (1)\;2 \log _e 2-2 & \quad (2)\;2-2 \log _e2 \\ (3)\;2 log_e 4 & \quad (4)\;\log _e 4 \end {array}\]