Question

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

Answer 1

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