Question

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1/1.3+1/3.5+15.7+...+1/2009.2011

 

Answer 1

1/.3 + 1/3.5 + 1/5.7 + ... + 1/2009.2011

= 1/2 . ( 2/1.3 + 2/3.5 + 2/5.7 + ... + 2/2009.2011)

= 1/2 . (1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/2009 - 1/2011)

= 1/2 . (1 - 1/2011)

= 1/2 . 2010/2011

= 1005/2011

Answer 2

\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2009.2011}\)

\(=\frac{1}{2}x\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2009}-\frac{1}{2011}\right)\)

\(=\frac{1}{2}x\left(1-\frac{1}{2011}\right)\)

\(=\frac{1005}{2011}\)