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1/1x2x3x4+1/2x3x4x5+1/3x4x5x6+1/4x5x6x7+1/5x6x7...

1/(1×2×3×4)+1/(2×3×4×5)+1/(3×4×5×6)+...+1/(7×8×9×10) =(1/3)×[1/(1×2×3)-1/(2×3×4)]+(1/3)×[1/(2×3×4)-1/(3×4×5)]+(1/3)×[1/(3×4×5)-1/(4×5×6)]+...+(1/3)×[1/(7×8×9)-1/(8×9×10)] =(1/3)×[1/(1×2×3)-1/(2×3×4)+1/(2×3×4)-1/(3×4×5)...

1/(1×2×3×4)+1/(2×3×4×5)+1/(3×4×5×6)+...+1/(7×8×9×10) =(1/3)×[1/(1×2×3)-1/(2×3×4)]+(1/3)×[1/(2×3×4)-1/(3×4×5)]+(1/3)×[1/(3×4×5)-1/(4×5×6)]+...+(1/3)×[1/(7×8×9)-1/(8×9×10)] =(1/3)×[1/(1×2×3)-1/(2×3×4)+1/(2×3×4)-1/(3×4×5)...

6/7

你在算算 是210个6

1×2×3×4+1=(2×3-1)^2=5^2. 2×3×4×5+1=(3×4-1)^2=11^2. 3×4×5×6+1=(4×6-1)^2=19^2. 4×5×6×7+1=(5×6-1)^2=29^2 即等于每式第二第三项相乘减一 所以11×12×13×14+1=(12×13-1)^2=155^2=24025

(n²+5n+5)²

1/6+1/24+1/60+1/120+1/210=20/120+5/120+2/120+1/120+1/210=7/30+1/210=50/210=5/21

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