1998/1998*1999+1998/1999*2000+1998/2000*2001+.+1998/2049*2050
=1998(1/1998*1999+1/1999*2000+1/2000*2001+...+1/2049*2050)
=1998((1/1998-1/1999)+(1/1999-1/2000)+(1/2000-1/2001)+...+(1/2049-1/2050))
=1998(1/1998-1/2050)
=1-1998/2050
=52/2050
=26/1025
1/1*4+1/4*7+1/7*10+1/10*13.+1/97*100
=((1-1/4)/3+(1/4-1/7)/3+(1/7-1/10)/3+...+(1/97-1/100)/3)
=(1-1/4+1/4-1/7+1/7-1/10+...+1/97-1/100)/3
=(1-1/100)/3
=(99/100)/3
=33/100