1/3+1/5+1/7+1/9+1/11+1/33+1/35+1/45+1/55+1/77=?

来源：学生作业帮编辑：神马作文网作业帮分类：数学作业时间：2024/11/16 19:10:48

1/3+1/5+1/7+1/9+1/11+1/33+1/35+1/45+1/55+1/77
=1/3+1/5+1/7+1/9+1/11+(1/3-1/11)/8+(1/5-1/7)/2
+(1/5-1/9)/4+(1/5-1/11)/6+(1/7-1/11)/4
=1/3+1/5+1/7+1/9+1/11+(1/3)/8-(1/11)/8+(1/5)/2-(1/7)/2+
(1/5)/4-(1/9)/4+(1/5)/6-(1/11)/6+(1/7)/4-(1/11)/4
=(1/3)*[1+1/8]
+(1/5)*[1+1/2+1/4+1/6]
+(1/7)*[1-1/2+1/4]
+(1/11)*[1-1/8-1/6-1/4]
+(1/9)*[1-1/4]
=(1/3)*(9/8)+(1/5)*(23/12)+(1/7)*(3/4)+(1/11)*(11/24)+(1/9)*(3/4)
=(1/3)*(9/8)+(1/5)*(23/12)+(1/7)*(3/4)+1/24+1/12
=(3/8)+(1/5)*(23/12)+(1/7)*(3/4)+1/8
=1/2+(1/5)*(23/12)+(1/7)*(3/4)
=(6*5*7+23*7+3*3*5)/(12*5*7)
=[210+161+45]/(12*5*7)
=416/(12*5*7)
=104/105

3/1+5/1+7/1+11/1+33/1+35/1+45/1+55/1+77/1=?（/表示分数线） 1+2+3+4+5+6+7+8+9+10+11+22+33+44+55+66+77+88+99=? 1+1/15+3+1/35+5+1/63+7+1/99+9+1/143+11+1/195=? 1/3+1/5+1/7+1/9+1/11+1/13+1/15= 已知(1/3-1/5)*1/2=1/15,（1/5-1/7)*1/2=1/35,(1/7-1/9)*1/2=1/63 (1/3+1/5+1/7+1/9)*(1/5+1/7+1/9+1/11)-(1/3+1/11+1/5+1/7+1/9)* (1-1/3)×(1-1/5)×(1-1/7)×(1-1/9)×(1-1/11))×(1-1/13)×(1-1/15)= 1+2+3+4+5+6+7+8+9+99+88+77+66+55+44+33+22+11 (1+1/15)+(3+1/35)+(5+1/63)+(7+1/99)+(9+1/143)+(11+1/195) 1/11+2/22+3/33+4/44+5/55+6/66+7/77+8/88+9/99-10/100+11/110+1 简算:1/1*3+1/3*5+1/5*7+1/7*9+1/9*11 1+1+2+3+4+5+6+7+8+9+11+622+33+44+55+66=?