1∕1×2×3+1∕2×3×4+1/4×5×6+1/6×7×8+1/8×9×10=
问题描述:
1∕1×2×3+1∕2×3×4+1/4×5×6+1/6×7×8+1/8×9×10=
答
1∕1×2×3+1∕2×3×4+1/3×4×5+1/4×5×6+1/5×6×7+1/6×7×8+1/7×8×9+1/8×9×10
=1/2×(1∕1×2-1/2×3+1∕2×3-1/3×4+1/3×4-1/4×5+1/4×5-1/5×6+1/5×6-1/6×7+1/6×7-1/7×8+1/7×8-1/8×9+1/8×9-1/9×10)
=1/2×(1/1×2-1/9×10)
=1/2×(1/2-1/90)
=1/2×22/90
=11/90