Question

99-97+95-93+91-89+...+7-5+3-1 怎样简便运算

Answer 1

解：99-97+95-93+91-89+…+7-5+3-1=（99-97）+（95-93）+（91-89）+…+（7-5）+（3-1）（共50个数组成25个减法算式）=2+2+2+…+2+2（共25个2相加）=2×25=50

Answer 2

1.原式=1*6-1/6-1/12-1/20-1/30-1/42-1/56
裂项后=6-1/(2*3)-1/(3*4)-1/(4*5)-1/(5*6)-1/(6*7)-1/(7*8)
=6-(1/2-1/3)-(1/3-1/4)-(1/4-1/5)-(1/5-1/6)-(1/6-1/7)-(1/7-1/8)
=6-1/2+1/3-1/3+1/4-1/4+1/5-1/5+1/6-1/6+1/7-1/7+1/8
=6-1/2+1/8
=11/2+1/8
=45/8

2.原式=99+95+91+...+7+3-97-93-89-...-5-1
观察后发现每次加减都等于2
即=2*[（99-3）/4+1]
=2*25
=50

3.原式=（784×321+784-213）/(784*321+571)
=（784×321+571）/(784*321+571)
=1

4.想不出来

5.原式=511*[(37*10101)/(73*10101)]
=511*37/73
=7*37
=259