www.5129.net > 1x2+2x3+3x4+4x5+5x6+6x7+7x8+8x9=

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

1x2 + 2x3 + 3x4 + ...... + n(n+1) = 1/3 * n(n+1)(n+2) 1x2+2x3+3x4+4x5+5x6+6x7+7x8+8x9 = 1/3 * 8 * 9 * 10 = 240

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

1x2+2x3+3x4+…+n(n+1) =1x(1+1)+2x(2+1)+3x(3+1)+…n(n+1) =(1^2+2^2+3^2+…+n^2)+(1+2+3+…+n) =n(n+1)(2n+1)/6+n(n+1)/2 =n(n+1)[(2n+1)+3]/6

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

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

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...

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

y=5x6+6x7+7x8+8x9+9x10+10x11+11x12 y=5*6+6*7+7*8+8*9+9*10+10*11+11*12 = 532

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...

1+2x3+4x5+6x7+8x9=4455 说明:在上面等号前加2个括号,使之等于4455 (1+2×3+4×5+6)×(7+8)×9==4455 7 7 7 7=10 在3个空处使用加减乘除 三个空处都要使用符号吗?如果都用,那应该没有答案.

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