1/3+1/15+1/35+1/63+……+1/399+1/4831/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90

1) = 1/3+ (1/3-1/5) +(1/5-1/7) + ..... +(1/21 - 1/23)
= 1/3 + 1/3 - 1/23 = 43/96
2) = 1/2+ (1/2-1/3) +(1/3-1/4) + ..... +(1/9 - 1/10)
= 1/2 + 1/2 - 1/10= 9/10

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