Question

这几道数学题怎么写

1、1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8
2、1/1*4+1/4*7+1/7*10+……+1/97*100
3、2/1*3+2/3*5+2/5*7+……+2/97*99
4、1/3+1/6+1/12+1/24+1/48+……+1/768
5、1/2+5/6+11/12+19/20+……+379/380

Answer 1

1、1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
=1/2-1/8=3/8
2、1/1*4+1/4*7+1/7*10+……+1/97*100
=1/3(1-1/4)+1/3(1/4-1/7)+1/3(1/7+1/10)+.......+1/3(1/97+1/100)
=1/3(1-1/4+1/4-1/7+....1/97-1/100)
=1/3(1-1/100)
=1/3*99/100
=33/100

3、2/1*3+2/3*5+2/5*7+……+2/97*99
=1-1/3+1/3-1/5+1/5-1/7+....+1/97-1/100
=1-1/100
=99/100
4、1/3+1/6+1/12+1/24+1/48+……+1/768
=2/3-1/768 =511/768
5、1/2+5/6+11/12+19/20+……+379/380
=1-1/2+1-1/6+1-1/12+1-1/20+.....+1-1/380
=19-(1/2+1/6+1/12+1/20+....+1/380)
=19-(1-1/2+1/2-1/3+1/3-1/4+.....+1/19-1/20)
=19-(1-1/20)
=19-19/20
=18又1/20