1/5×1/6=1/5-1/6,1/6×1/7=1/6-1/7,1/7×1/8=1/7-1/8,1/8×1/9=1/8-1/91/9×1/10=1/9-1/101/5×1/6＋1/6×1/7＋1/7×1/8＋1/8×1/9＋1/9×1/10=1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10=1/5-1/10=2/10-1/10=1/10...為什么1/n(n+1)=1/n-1/(n+1)呢？還是有些不懂……因?yàn)?1/n)-1/(n+1)=(n+1)/[n(n+1)]-n/[n(n+1)]---------通分=[(n+1)-n]/[n(n+1)]=1/[n(n+1)]1/[n(n+1)]=(1/n)-1/(n+1)假設(shè)取個(gè)特殊值，n=3,也就是1/(3×4)=1/3-1/4有疑問(wèn)歡迎繼續(xù)追問(wèn)，祝學(xué)習(xí)進(jìn)步！