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1x2+2x3+3x4+4x5+5x6+6x7+7x8+8x9=

1x2+2x3+3x4+4x5+5x6+6x7+7x8+8x9.....+29x30=8990

1x2+2x3+3x4+4x5+5x6+6x7+7x8+8x9+9x10+10x11 =10×(10+1)×(10+2)÷3 =10×11×12÷3 =110×12÷3 =1320÷3 =440

3÷(3x4)x(4x5)÷(5x6)x(6x7)÷(7x8)x(8x9)=(3÷3)÷4×4×5÷5÷6×6×7÷7÷8×8×9=1×9=9

1×2+2×3+...+8×9 太长了,就不抄全了。 =1×(1+1)+2×(2+1)+...+8×(8+1) =1²+2²+...+8²+1+2+...+8 =8×9×17/6 +8×9/2 =204+36 =240 利用公式: 1+2+...+n=n(n+1)/2 1²+2²+...+n²=n(n+1)(2n+1)/6

1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8+1/8x9+1/9x10 =1-1/2+1/2-1/3+1/3-....-1/9+1/9-1/10 =1-1/10 =9/10

如图

1/4X5 + 1/5X6 + 1/6X7 + 1/7X8 + 1/8X9 + 1/9X10 = (1/4 - 1/5) + (1/5 - 1/6) + (1/6 - 1/7) + (1/7 - 1/8) + (1/8 -1/9) + (1/9 - 1/10) = 1/4 - 1/10 = 3/20

1x2/1+2x3/1+3x4/1+4x5/1+5x6/1+6x7/1+7x8/1+8x9/1+9x10/1 =1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90 =(1-1/2)+(1/2-1/3)+……+(1/8-1/9)+(1/9-1/10) =1-1/10 =9/10

因为an=n*(n-1)/n+1 所以每个数可以看成2/3+(1+2/4)+(2+2/5)+(3+2/6)...+(8+2/11)= 1+2+3...+8+2/3+2/4+2/5...+2/11=36+2*(1/3+1/4+1/5+...1/11) 因为后面的那个是一个发散数列,好像没有求和公式,所以只能同分计算,当然可以把简单...

解:①2x3/1+3x4/1+4x5/1+5x6/1+6x7/1+7x8/1+8x9/1+9x10/1+10x11/1 =6+12+20+30+42+56+72+90+110 =(6+12+72)+(20+30+90+110)+(42+56) =90+250+98 =438 ②如果楼主原意这样,那么解法不同: 1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8+1/8x9+1/9x10+1/10...

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