问题标题:
1155X(5/2X3X4+7/3X4X5+```````+17/8X9X10+19/9X10X11)=?
问题描述:
1155X(5/2X3X4+7/3X4X5+```````+17/8X9X10+19/9X10X11)=?
李春燕回答:
因为5/2×3×4=(2+3)/2×3×4=1/3×4+1/2×4
1/3×4=1/3-1/41/2×4=1/2(1/2-1/4)
原式=1155×[(1/3×4+1/2×4)+(1/4×5+1/3×5)+…+(1/9×10+
1/8×10)+(1/10×11+1/9×11)]
=1155×[(1/3×4+1/4×5+…+1/9×10+1/10×11)+(1/2×4+
1/3×5+…+1/8×10+1/9×11)]
=1155×[(1/3-1/4+1/4-1/5+…+1/9-1/10+1/10-1/11)+
1/2(1/2-1/4+1/3-1/5+…+1/8-1/10+1/9-1/11)]
=1155×[(1/3-1/11)+1/2(1/2+1/3-1/10-1/11)]
=1155×(1/3-1/11+1/4+1/6-1/20-1/22)
=1155×(1/2+1/5-3/22)
=1155×(7/10-3/22)
=1155×124/220
=651
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