Question

简便运算（要有过程)

1/4+1/28+1/70+1/130+1/208
1/3X5+1/5X7+1/7X9+.....+1/97X99
1/2+1/6+1/12+1/20+1/30+1/42
1/4X5+1/5X6+1/6X7+.....+1/39X40
1/10X11+1/11X12+1/12X13+1/13X14+1/14X15

Answer 1

1/4+1/28+1/70+1/130+1/208
=（1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16）÷3
=（1-1/16）÷3
=15/16÷3
=5/16
1/3X5+1/5X7+1/7X9+.....+1/97X99
=（1/3-1/5+1/5-1/7+1/7-1/9+……+1/97-1/99）÷2
=（1/3-1/99）÷2
=32/99÷2
=16/99
1/2+1/6+1/12+1/20+1/30+1/42
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-1/7
=6/7
1/4X5+1/5X6+1/6X7+.....+1/39X40
=1/4-1/5+1/5-1/6+1/6-1/7+……+1/69-1/40
=1/4-1/40
=9/40
1/10X11+1/11X12+1/12X13+1/13X14+1/14X15
=1/10-1/11+1/11-1/12+1/12-1/13+1/13-1/14+1/14-1/15
=1/10-1/15
=1/30

Answer 2

1/4+1/28+1/70+1/130+1/208
=1/3*（1/3-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16）
=1/3*（1/3-1/16）
=1/3*13/48
=13/144
1/3X5+1/5X7+1/7X9+.....+1/97X99
=1/2*（1/3-1/5+1/5-1/7+1/7-1/9+1/9+....+1/97-1/99
=1/2*（1/3-1/99）
=1/2*32/99
=16/99
1/2+1/6+1/12+1/20+1/30+1/42
=1-1/2+1/2-1/2+1/3-1/3+.....+1/6-1/7
=1-1/7
=6/7
1/4X5+1/5X6+1/6X7+.....+1/39X40
=1/4-1/5+1/5-1/6+1/6-1/7+........+1/39-1/40
=1/4-1/40
=9/40
1/10X11+1/11X12+1/12X13+1/13X14+1/14X15
=1/10-1/11+1/11-1/12+1/12+......+1/14-1/15
=1/10-1/15
=1/30

Answer 3

1、原式=1/1×4+1/4×7+1/7×10+1/10×13+1/13×16
=1/3(1-1/4)+1/3(1/4-1/7)+1/3(1/7-1/10)+1/3(1/10-1/13)+1/3(1/13-1/16)
=1/3(1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16)
=1/3(1-1/16)
=5/16
2、 原式=1/2[1/3-1/5+1/5-1/7+1/7-1/9+...+1/97-1/99]
=1/2(1/3-1/99)
=16/99
3、原式=1/1×2+1/2×3+1/3×4+1/4×5+1/5×6+1/6×7
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-1/7
=6/7
4、原式=1/4-1/5+1/5-1/6+1/6-1/7+...+1/39-1/40
=1/4-1/40
=9/40
5、原式=1/10-1/11+1/11-1/12+1/12-1/13+1/13-1/14+1/14-1/15
=1/10-1/15
=1/30