Question

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

(-1×1/2)+(-1/2×1/3)+(-1/3×1/4)+…+(-1/2012×1/2013) 求大神指导~

Answer 1

将 (1-1/2)+(1/2-1/3)+(1/3-1/4)......+(1/1999-1/2000)分解（去括号）为1-2/1+2/1-3/1+3/1......+1/1999-1/2000。因为减1-2/1又加2/1，所以+2/1与-2/1互相抵消，-3/1+3/1也抵消。。。。+1/19991与-/1999互相抵消。。1没得抵消1/2000也没得抵消，只好照 算。所以：
(1-1/2)+(1/2-1/3)+(1/3-1/4)......+(1/1999-1/2000)
=1-2/1+2/1-3/1+3/1......+1/1999-1/2000
=1-（2/1-2/1）-（3/1-3/1）-.......（1/1999-1/1999）-1/2000
=1-1/2000
=1999/2000

追问

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