$$\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+\frac{2}{9\times11}$$
$\frac{10}{11}\approx 0.909090909$
$$\frac{2}{3}+\frac{2}{3\times 5}+\frac{2}{5\times 7}+\frac{2}{7\times 9}+\frac{2}{9\times 11}$$
$$\frac{2}{3}+\frac{2}{15}+\frac{2}{5\times 7}+\frac{2}{7\times 9}+\frac{2}{9\times 11}$$
$$\frac{10}{15}+\frac{2}{15}+\frac{2}{5\times 7}+\frac{2}{7\times 9}+\frac{2}{9\times 11}$$
$$\frac{10+2}{15}+\frac{2}{5\times 7}+\frac{2}{7\times 9}+\frac{2}{9\times 11}$$
$$\frac{12}{15}+\frac{2}{5\times 7}+\frac{2}{7\times 9}+\frac{2}{9\times 11}$$
$$\frac{4}{5}+\frac{2}{5\times 7}+\frac{2}{7\times 9}+\frac{2}{9\times 11}$$
$$\frac{4}{5}+\frac{2}{35}+\frac{2}{7\times 9}+\frac{2}{9\times 11}$$
$$\frac{28}{35}+\frac{2}{35}+\frac{2}{7\times 9}+\frac{2}{9\times 11}$$
$$\frac{28+2}{35}+\frac{2}{7\times 9}+\frac{2}{9\times 11}$$
$$\frac{30}{35}+\frac{2}{7\times 9}+\frac{2}{9\times 11}$$
$$\frac{6}{7}+\frac{2}{7\times 9}+\frac{2}{9\times 11}$$
$$\frac{6}{7}+\frac{2}{63}+\frac{2}{9\times 11}$$
$$\frac{54}{63}+\frac{2}{63}+\frac{2}{9\times 11}$$
$$\frac{54+2}{63}+\frac{2}{9\times 11}$$
$$\frac{56}{63}+\frac{2}{9\times 11}$$
$$\frac{8}{9}+\frac{2}{9\times 11}$$
$$\frac{8}{9}+\frac{2}{99}$$
$$\frac{88}{99}+\frac{2}{99}$$
$$\frac{88+2}{99}$$
$$\frac{90}{99}$$
$$\frac{10}{11}$$
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$\frac{2 \cdot 5}{11} = 0.9090909090909091$
