Question

二分之五+六分之五+十二分之五+二十分之五+.+九千九百分之五

Answer 1

5/2 + 5/6 + 5/12 + 5/20 + … + 5/9900

=5(1/2 + 1/6 + 1/12 + 1/20 + … + 1/9900 )

=5[1/(1*2) + 1/(2*3) + 1/(3*4) + … +1/(99*100)]

=5( 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + … + 1/99 - 1/100 )

= 5( 1 - 1/100)

= 5×99/100

= 99/22