(-1×1/2)+(-1/2×1/3)+(-1/3×1/4)+…+(-1/2012×1/2013) 求大神指导~
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![(-1×1/2)+(-1/2×1/3)+(-1/3×1/4)+…+(-1/2012×1/2013) 求大神指导~](/uploads/image/z/803557-37-7.jpg?t=%28-1%C3%971%2F2%29%2B%28-1%2F2%C3%971%2F3%29%2B%28-1%2F3%C3%971%2F4%29%2B%E2%80%A6%2B%28-1%2F2012%C3%971%2F2013%29++++%E6%B1%82%E5%A4%A7%E7%A5%9E%E6%8C%87%E5%AF%BC%7E)
(-1×1/2)+(-1/2×1/3)+(-1/3×1/4)+…+(-1/2012×1/2013) 求大神指导~
(-1×1/2)+(-1/2×1/3)+(-1/3×1/4)+…+(-1/2012×1/2013) 求大神指导~
(-1×1/2)+(-1/2×1/3)+(-1/3×1/4)+…+(-1/2012×1/2013) 求大神指导~
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