1\frac{1}{x_n+1}= \frac{1}{x_{n}}-\frac{1}{x_{n+1}}
\frac{1}{x_1+1}+\frac{1}{x_2+1}+....+\frac{1}{x_{2008}+1} = \frac{1}{x_1}-\frac{1}{x_{2009}}
i feel that the question has some printing errors
i am typing the question as given in the book
consider \ the \ sequence \ x_n \ defined \ by \ \\ x_1 = \frac{1}{2} ,x_{n+1}=x_n^2 + x_n \\ define \ S = \frac{1}{x_1 +1}+\frac{1}{x_2 +1}+ ............ + \frac{1}{x_{2008}} \\ then \ [S] \ ? \\ [.]\ is \ GIF
answer given is 1
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