1/2x4+1/4x8+1/6x8+…+1/2012x2014

如题所述

1/2×4+1/4×8+1/6×8+...+1/2012×2014
=1/2×(1/2-1/4)+1/2×(1/4-1/8)+...+1/2×(1/2012-1/2014)
=1/2×(1/2-1/4+1/4-1/8+...+1/2012-1/2014)
=1/2×(1/2-1/2014)
=1/2×(1007/2014-1/2014)
=1/2×1006/2014
=503/2014
此题属于裂项问题,主要涉及的公式有:
①1/n(n+1)=1/n-1/(n+1)
②1/n(n+k)=1/k[1/n-1/(n+k)]
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