Question

1乘以2乘以3乘以4的积分之1加上2乘以3乘以4乘以5的积分之1加上3乘以4乘以5乘以6的积分之1

一直加到7乘以8乘以9乘以10的积分之1 答案是多少？要求简算 能写出具体的过程 谢谢

Answer 1

1/(1x2x3x4)+1/(2x3x4x5)+1/(3x4x5x6)+……+1/(7x8x9x10)
=1/3x[1/(1x2x3)-1/(2x3x4)+1/(2x3x4)-1/(3x4xx5)+1/(3x4x5)-1/(4x5x6)+……+1/(7x8x9)-1/(8x9x10)]
=1/3x[1/(1x2x3)-1/(8x9x10)]
=1/3x[1/6-1/720]
=1/3x119/720
=119/2160