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1/(2×3) + 1/(3×4) + 1/(4×5) + 1/(5×6) + ... + 1/(2007×2008) = ...
1/(2×3) + 1/(3×4) + 1/(4×5) + 1/(5×6) + ... + 1/(2007×2008) = ...
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1/(3 x 4) = 1/3 - 1/4
1/(4 x 5) = 1/4 - 1/5
1/(5 x 6) = 1/5 - 1/6
.....
.....
1/(2007 x 2008) = 1/2007 - 1/2008
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1/(2x3) + 1/(3x4) + 1/(4x5) + ... + 1/(2007x2008) = 1/2 - 1/2008 = 1004/2008 - 1/2008 = 1003/2008
1/(3 x 4) = 1/3 - 1/4
1/(4 x 5) = 1/4 - 1/5
1/(5 x 6) = 1/5 - 1/6
.....
.....
1/(2007 x 2008) = 1/2007 - 1/2008
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1/(2x3) + 1/(3x4) + 1/(4x5) + ... + 1/(2007x2008) = 1/2 - 1/2008 = 1004/2008 - 1/2008 = 1003/2008