超难计算题,天才留步!1+1/3+1/6+1/10+…+1/2009×1004=?quickly quickly quickly

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超难计算题,天才留步!1+1/3+1/6+1/10+…+1/2009×1004=?quicklyquicklyquickly超难计算题,天才留步!1+1/3+1/6+1/10+…+1/2009×100

超难计算题,天才留步!1+1/3+1/6+1/10+…+1/2009×1004=?quickly quickly quickly
超难计算题,天才留步!
1+1/3+1/6+1/10+…+1/2009×1004=?
quickly quickly quickly

超难计算题,天才留步!1+1/3+1/6+1/10+…+1/2009×1004=?quickly quickly quickly
1+1/3+1/6+1/10+.+1/(2009×1004)
=2/2+2/(2×3)+2/(3×4)+2/(4×5)+.+2/(2008×2009)
=2×〔1/2+1/(2×3)+1/(3×4)+1/(4×5)+.+1/(2008×2009)]
=2×(1/2+1/2-1/3+1/3-1/4+1/4-1/5+.+1/2008-1/2009)
=2×(1-1/2009)
=2×2008/2009
=4016/2009

很简单!:
1+1/3+1/6+1/10+......+1/(2009×1004)
=2/2+2/(2×3)+2/(3×4)+2/(4×5)+.....+2/(2008×2009)
=2×〔1/2+1/(2×3)+1/(3×4)+1/(4×5)+......+1/(2008×2009)]
=2×(1/2+1/2-1/3+1/3-1/4+1/4-1/5+......+1/2008-1/2009)
=2×(1-1/2009)
=2×2008/2009
=4016/2009