2/4×6+2/6×8+2/8×10+2/10×12+2/12×14的简便算法拜托各位了 3Q

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2/4×6+2/6×8+2/8×10+2/10×12+2/12×14的简便算法拜托各位了 3Q
2/4×6+2/6×8+2/8×10+2/10×12+2/12×14的简便算法拜托各位了 3Q

2/4×6+2/6×8+2/8×10+2/10×12+2/12×14的简便算法拜托各位了 3Q
求和公式:1/2+1/2*1/3+1/3*1/4+...+1/n*1/(n+1)=(n-1)/n --------------------------------------------------------------------------------------- 2/(4×6)+2/(6×8)+2/(8×10)+2/(10×12)+2/(12×14) = 2/(2×2×2×3)+2/(2×2×3×4)+2/(2×2×4×5)+2/(2×2×5×6)+2/(2×2×6×7) =1/[2×(2×3)]+1/[2×(3×4)]+1/[2×(4×5)]+1/[2×(5×6)]+1/[2×(6×7)] =1/2×[1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6)+1/(6×7)] //根据公式n=6 =1/2×(5/6-1/2) //根据公式(n-1)/n=5/6 =1/2×1/3 =1/6