3/2-5/6+7/12-9/20+11/30-13/42+15/56-17/72

如题所述

第1个回答 2022-11-18

3/2-5/6+7/12-9/20+11/30-13/42+15/56-17/72

原式=（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)
=1-1/9
=8/9

3/2-5/6+7/12-9/20+11/30-13/42+15/56-17/72=

3/2-5/6+7/12-9/20+11/30-13/42+15/56-17/72
=(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)
=1-1/9
=8/9

3/2-5/6+7/12-9/20+11/30-13/42+15/56-17/72+19/90=？

原式=(2+1)/(2*1)-(3+2)/(3*2)+(4+3)/(4*3)-(5+4)/(5*4)+(6+5)/(6*5)-(6+7)/(6*7)+(7+8)/(7*8)-(8+9)/(8*9)+(9+10)/(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+1/3+1/3+1/5+1/5+1/7+1/7+1/9+1/9+1/10 =结果自己算、、、太麻烦了、

3/2-5/6+7/12-9/20+11/30-13/42+15/56-17/72+19/90。。。求解～急

3/2-5/6+7/12-9/20+11/30-13/42+15/56-17/72+19/90
=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+1/2-1/2-1/3+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
=11/10

3/2-5/6+7/12-9/20+11/30-13/42+15/56=?

=3/2-5/6+7/12-9/20+11/30-13/42+15/56
=(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+1/8
=9/8

3/2-5/6+7/12-9/20+11/30-13/42+15/56

=(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+1/8
=1又1/8

1+1/2-5/6+7/12-9/20+11/30-13/42+15/56-17/72+19/90

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=11/10

1+1/2-5/6+7/12-9/20+11/30-13/42+15/56-17/72+19/90
=5/4-9/20+11/30-13/42+15/56-17/72+19/90
=5/4-(4+5)/4*5+(5+6)/5*6-(6+7)/6*7+(7+8)/7*8-(8+9)/8*9+(9+10)/9*10
=5/4-1/4-1/5+1/5+1/6-1/6-1/7+1/7+1/8-1/8-1/9+1/9+1/10
=1+1/10
=11/10.

1-5/6+7/12-9/20+11/30-13/42+15/56-17/72=？

1-5/6+7/12-9/20+11/30-13/42+15/56-17/72+19/90
=1-(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)
=1-1/2+1/10
=3/5

1-5/6+7/12-9/20+11/30-13/42+15/56-17/72+19/90

1-5/6+7/12-9/20+11/30-13/42+15/56-17/72+19/90
=1-(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)
=1-1/2+1/10
=3/5
这样可以么？

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