Question

奥数碰碰车:计算:1/4x5+1/5x6+1/6x7+1/7x8......+1/39x40=?

Answer 1

1/4x5+1/5x6+1/6x7+1/7x8......+1/39x40
=1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+……+1/39-1/40
=1/4-1/40
=9/40

1/1x2x3+1/2x3x4+1/3x4x5+......+1/8x9x10
=（1/1x2-1/2x3+1/2x3-1/3x4+1/3x4-1/4x5+......+1/8x9-1/9x10）÷2
=（1/1x2-1/9x10）÷2
=（1/2-1/90）÷2
=22/45÷2
=11/45

Answer 2

-1/（4*5）=1/4-1/5
1/（5*6）=1/5-1/6
……
1/（39*40）=1/39-1/40

原式= 1/4-1/5+1/5-1/6+……+1/39-1/40
=1/4-1/40
=9/40

追问

计算：1/1x2x3+1/2x3x4+1/3x4x5+......+1/8x9x10=？

Answer 3

1/4x5+1/5x6+1/6x7+1/7x8......+1/39x40=(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+...+(1/39-1/40)
=1/4-1/5+1/5-1/6+1/6-1/7+.....+1/39-1/40
=1/4-1/40=9/40