Question

\(F=\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+\frac{3}{11\cdot14}+...+\frac{3}{2006\cdot2009}\)

Answer 1

\(F=\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+...+\frac{3}{2006.2009}\)

\(F=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{2006}-\frac{1}{2009}\)

\(F=\frac{1}{5}-\frac{1}{2009}\)

\(F=\frac{2004}{10045}\)

Answer 2

\(F=\frac{3}{5.8}+\frac{3}{8.11}+\frac{1}{11.14}+...+\frac{3}{2006.2009}\)

\(F=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{2006}-\frac{1}{2009}\)

\(F=\frac{1}{5}-\frac{1}{2009}\)

\(F=0\)

Answer 3

F = 1/5 - 1/8 + 1/8 - 1/11 +,,,+1/2006 - 1/2009
F = 1/5 - 1/2009
F = 2008/10044
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Answer 4

\(F=\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+\frac{3}{11\cdot14}+...+\frac{3}{2006\cdot2009}\)

\(F=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{2006}-\frac{1}{2009}\)

\(F=\frac{1}{5}-\frac{1}{2009}\)

\(F=\frac{2004}{10045}\)