(负1×1/2)+(负1/2×1/3)+(负1/3×1/4)……(负1/2012×1/2013)等于多少?
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(负1×1/2)+(负1/2×1/3)+(负1/3×1/4)……(负1/2012×1/2013)等于多少?
![(负1×1/2)+(负1/2×1/3)+(负1/3×1/4)……(负1/2012×1/2013)等于多少?](/uploads/image/z/16834279-31-9.jpg?t=%28%E8%B4%9F1%C3%971%2F2%29%2B%28%E8%B4%9F1%2F2%C3%971%2F3%29%2B%28%E8%B4%9F1%2F3%C3%971%2F4%29%E2%80%A6%E2%80%A6%28%E8%B4%9F1%2F2012%C3%971%2F2013%29%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%3F)
(负1×1/2)+(负1/2×1/3)+(负1/3×1/4)……(负1/2012×1/2013)
= -(1×1/2+1/2×1/3+……+1/2012×1/2013)
= -(1-1/2+1/2-1/3+……+1/2012-1/2013)
= -(1-1/2013)
= -2012/2013
= -(1×1/2+1/2×1/3+……+1/2012×1/2013)
= -(1-1/2+1/2-1/3+……+1/2012-1/2013)
= -(1-1/2013)
= -2012/2013
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