(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?
(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?
(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

(负1×1/2)+(负1/2×1/3)+(负1/3×1/4)……(负1/2012×1/2013)
=(1/2-1)+(1/3-1/2)+(1/4-1/3)+...+(1/2013-1/2012)
=1/2013-1
=-2012/2013

(负1×1/2)+(负1/2×1/3)+(负1/3×1/4)……(负1/2012×1/2013)
=1/2和负1/2互相低了,后面也是一样
=就剩负1×1/2013
=负1/2013