简算(要有过程)(1)1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132(2)1/1*5+1/5*9+1/9*13+...+1/97*101(3)2又1/2*5+4又1/5*8+6又1/8*11+...+102又1/152*155(4)1/4+30又1/28+50又1/70+70又1/130+90又1/208(5)14/15+34/35+62/63+98/99+142/1
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![简算(要有过程)(1)1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132(2)1/1*5+1/5*9+1/9*13+...+1/97*101(3)2又1/2*5+4又1/5*8+6又1/8*11+...+102又1/152*155(4)1/4+30又1/28+50又1/70+70又1/130+90又1/208(5)14/15+34/35+62/63+98/99+142/1](/uploads/image/z/431938-10-8.jpg?t=%E7%AE%80%E7%AE%97%28%E8%A6%81%E6%9C%89%E8%BF%87%E7%A8%8B%EF%BC%89%281%291%2F12%2B1%2F20%2B1%2F30%2B1%2F42%2B1%2F56%2B1%2F72%2B1%2F90%2B1%2F110%2B1%2F132%EF%BC%882%EF%BC%891%2F1%2A5%2B1%2F5%2A9%2B1%2F9%2A13%2B...%2B1%2F97%2A101%283%292%E5%8F%881%2F2%2A5%2B4%E5%8F%881%2F5%2A8%2B6%E5%8F%881%2F8%2A11%2B...%2B102%E5%8F%881%2F152%2A155%EF%BC%884%EF%BC%891%2F4%2B30%E5%8F%881%2F28%2B50%E5%8F%881%2F70%2B70%E5%8F%881%2F130%2B90%E5%8F%881%2F208%EF%BC%885%EF%BC%8914%2F15%2B34%2F35%2B62%2F63%2B98%2F99%2B142%2F1)
简算(要有过程)(1)1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132(2)1/1*5+1/5*9+1/9*13+...+1/97*101(3)2又1/2*5+4又1/5*8+6又1/8*11+...+102又1/152*155(4)1/4+30又1/28+50又1/70+70又1/130+90又1/208(5)14/15+34/35+62/63+98/99+142/1
简算(要有过程)
(1)1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132
(2)1/1*5+1/5*9+1/9*13+...+1/97*101
(3)2又1/2*5+4又1/5*8+6又1/8*11+...+102又1/152*155
(4)1/4+30又1/28+50又1/70+70又1/130+90又1/208
(5)14/15+34/35+62/63+98/99+142/143+194/195+254/255+322/323
(6)4/3+16/15+36/35+64/63+100/99+144/143+196/195+256/255+324/323+400/300
(7)1/2+5/6+11/12+19/20+29/30+...+9701/9702+9899/9900
(8)1-5/6+7/12-9/20+11/30-13/42+15/56-17/72+19/90-21/110
简算(要有过程)(1)1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132(2)1/1*5+1/5*9+1/9*13+...+1/97*101(3)2又1/2*5+4又1/5*8+6又1/8*11+...+102又1/152*155(4)1/4+30又1/28+50又1/70+70又1/130+90又1/208(5)14/15+34/35+62/63+98/99+142/1
(2)1/4(1-1/5+1/5-1/9+1/9-1/13.+1/97-1/101)=1/4(1-1/101)=25/101
(3)整数分成一列求和,分数部分和(2)类似,提取一个1/3
(4)基本和3一样,分数部分提取一个1/3 4=1X4 28=4X7 70=7X10 130=10X13 208=16X13
(5)14/15=1-1/15=1-1/2(1/3-1/5) 其他同理
有些很类似
总结一个分数的式子 1/a-1/b=(b-a)/ab
反之1/ab=[1/(b-a)]X(1/a-1/b)
如果一个系列的数都可以分成两个数的积,又这些数的差(b-a)相同,就可以结合简便计算了