Question

1除以2乘3乘4乘5加上1除以3乘4乘5乘6一直加到1除以1除以97乘98乘99乘100的和是多少

Answer 1

1/2X3X4X5+1/3X4X5X6+1/4X5X6X7.1/97X98X99X100=?

=1/3[1/2*3*4-1/3*4*5]+1/3[1/3*4*5-1/4*5*6]+1/3[1/4*5*6-1/5*6*7]+...+1/3[1/97*98*99-1/98*99*100]

=1/3[1/2*3*4-1/98*99*100]

=1/3*40424/98*99*100

=5053/3*49*99*25