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1X2X1/3+2X3X1/4+3X4X1/5+4X5X1/6+5X6X1/7+6X7X1/8...

1260

∵1*2*3=1/4*(1*2*3*4-0*1*2*3) 2*3*4=1/4*(2*3*4*5-1*2*3*4) 3x4x5=1/4x (3x4x5x6-2x3x4x5) ………… 7*8*9=1/4*(7*8*9*10-6*7*8*9) ∴1*2*3+2*3*4+……+7*8*9=1/4*7*8*9*10=1260

1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6++1/8x9x10 =1-1/2-1/2(1-1/3)+1/2-1/3-1/2(1/2-1/4)+1/3-1/4-1/2(1/3-1/5)+1/4-1/5-1/2(1/4-1/6)+.+1/8-1/9-1/2(1/8-1/10)=1-1/9-1/2(1+1/2-1/9-1/10)=173/360

1.7/302.大筐0、中筐40、小筐60大筐5、中筐32、小筐63大筐10、中筐24、小筐66大筐15、中筐16、小筐69大筐20、中筐8、小筐72大筐25、中筐0、小筐753x+2y+1/3*Z=100x+y+z=100转换:8x+5y=200则x、y为0-100之间自然数由

=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)=1/2*(1/1*2-1/5*6)=7/30

1/1x2x3+1/2x3x4+1/3x4x5+1/4x5x6++1/48x49x50=48*51÷(4*49*50)=306/1225

1/(n * (n + 1) * (n + 2)) = 1/ 2 * [1/(n * (n + 1)) - 1/((n + 1) * (n + 2))]所以= 1/2 * (1/(1 * 2) - 1/(2 * 3) + 1/(2 * 3) - 1/(3 * 4) ++ 1/(9 * 10) - 1/(10 * 11))= 1/2 * (1/2 - 1/110)= 27/110

(1*4+2)/4+(2*5+2)/5+(3*6+2)/6+(4*7+2)/7就想到这,得睡觉了!

解1/(1+2+3)+1/(2+3+4)+1/(3+4+5)……+1/(99+100+101) =1/6+1/9+1/12+1/15..+1/300 =1/3*(1/2+1/3..+1/99+1/100) =1/3*4.18737751763961 =1.39579250587987

5分之2

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