1.原式=1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11)+1/(11x13)+1/(11*15)+1/(15*17)+1/(17*19)+1/(21*23)
=(1-2/3)+(2/3-3/5)+(3/5-4/7)+(4/7-5/9)+(5/9-6/11)+(6/11-7/13)+(7/13-9/15)+(9/15-11/17)+(11/17-13/19)+(13/19-15/21)+(15/21-17/23)
=1-17/23
=6/23
2.
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)+1/(8*9)+1/(9*10)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
=1-1/10
=9/10