脱式计算：1/3*7+1/7*11+1/11*15+……+1/55*59拜托了各位 谢谢
脱式计算：1/3*7+1/7*11+1/11*15+……+1/55*59拜托了各位 谢谢
你好！首先找出规律即可 1/n(n+4)=1/4 [1/n--1/(n+4)] 所以： 1/3*7+1/7*11+1/11*15+……+1/55*59 =（1/3--1/7）+(1/7--1/11)+-----+(1/51--1/55)+(1/55--1/59) =1/3 --(1/7--1/7)--(1/11--1/11)---(1/55--1/55)--1/59 =1/3--1/59 =54/177 不懂可以继续追问，望采纳，谢谢！
1/3×7＋1/7×11＋1/11×15＋……＋1/55×59
=1/4(1/3-1/7+1/7-1/11....+1/55-1/59)
=1/4*(1/3-1/59)
14/177 没错a。。
1/3*7+1/7*11+1/11*15+……1/103*107
4*(1/3-1/7+1/7-1/11+1/11-1/13……-1/103+1/103-1/107)=4*(1/3-1/107)=416/321
1/3*7+1/7*11+1/11*15+······+1/99*103
= (1/3 - 1/7 + 1/7 - 1/11.....+ 1/99 - 1/103) * 1/4
= (1/3 - 1/103) * 1/4
= 25/309
1/3*7+1/7*11+1/11*15+...+1/55*59=?
因为1/3*7=1/21=1/4*（1/3-1/7）
所以，原式=1/4*（1/3-1/7）+1/4*(1/7-1/11)+……1/4*(1/55-1/59)
=1/4(1/3-1/7+1/7-1/11+……1/55-1/59)
=1/4*(1/3-1/59)
=14/177
初一数学奥数题求1/3*7+1/7*11+1/11*15+……+1/55*59
1/3*7=1/4(1/3-1/7)
1/7*11=1/4(1/7-1/11)
...
原式=1/4[(1/3-1/7)+(1/7-1/11)+(1/11-1/15)+...+(1/55-1/59)]
=1/4(1/3-1/59)
=1/4*(59-3)/177
=14/177
观察;1/3*7=(1/3-1/7)*1/4,1/7*11=(1/7-1/11)*1/4,计算：1/3*7+1/7*11+1/11*15+...+1/55*99
1/3*7+1/7*11+1/11*15+...+1/55*59
=(1/3-1/7)*1/4+(1/7-1/11)*1/4+...+（1/55-1/59）*1/4
=（1/3-1/59）*1/4
=14/3*39
=14/177
1/3*7+ 1/7/11+1/11*15+..............+1/55*59
1/3*7+ 1/7*11+1/11*15+..............+1/55*59
=1/4*(1/3-1/7)+1/4*(1/7-1/11)+1/4*(1/11-1/15)+......+1/4*(1/55-1/59)
=1/4*(1/3-1/7+1/7-1/11+1/11-1/15+......+1/55-1/59)
=1/4*(1/3-1/59)
=1/4*56/177
=14/177
1/3*7+1/7*11+1/11*15+...+1/25*39
1/3*7+1/7*11+1/11*15+...+1/25*39
=1/4*(1/3-1/7)+1/4*(1/7-1/11)+1/4*(1/11-1/15)+...+1/4*(1/25-1/29)
=1/4*(1/3-1/7+1/7-1/11+1/11-1/15+...+1/25-1/29)
=1/4*(1/3-1/29)
=1/4*26/87
=13/174
计算:1/3*5+1/5*7+1/7*9+1/9*11+1/11*13
解：1/3*5+1/5*7+1/7*9+1/9*11+1/11*13
＝1/2×﹙1/3－1/5＋1/5－1/7＋1/7－1/9＋1/9－1/11＋1/11－1/13﹚
＝1/2×﹙1/3－1/13﹚
＝1/2×10/39
＝5/39.
