1乘2分之29+2乘3分之29+……+28乘29分之29 等于多少
问题描述：
1乘2分之29+2乘3分之29+……+28乘29分之29
等于多少
答
29/(1x2)+29/2x3+……+29/(28x29)
=29x[1/(1x2)+1/2x3+……+1/(28x29)]
=29x[1-1/2+1/2-1/3+1/3-1/4+.......+1/28-1/29]
=29x(1-1/29)
=29x28/29
=28
答
29/(1x2)+29/2x3+……+29/(28x29)
=29x[1/(1x2)+1/2x3+……+1/(28x29)]
=29x[1-1/2+1/2-1/3+1/3-1/4+.......+1/28-1/29]
=29x(1-1/29)
=29x28/29
=28
其实就是裂项相消求和
祝你学习进步！
答
29/(1*2)+29/(2*3)+29/(3*4)+.29/(28*29)
=29[1/(1*2)+1/(2*3)+1/(3*4).+1/(28*29)]
=29[1/1-1/2+1/2-1/3+1/3-1/4+.+1/28-1/29]
=29[1-1/29]
=29[(29-1)/29]
=28
1乘2分之29+2乘3分之29+……+28乘29分之29 等于28.