One by two plus two by three plus three by four plus 49 by 50

One by two plus two by three plus three by four plus 49 by 50

1/2+1/6+1/12.+1/(49*50)=1-1/2+1/2-1/3+1/3-1/4+.-1/49+1/49-1/50
=1-1/50=49/50

(1-1 / 50) times (1-1 / 49) How much is multiplied by (1 / 2-1), there must be a process

(1 / 50-1) by (1 / 49-1); (1 / 3-1) by (1 / 2-1) =?
=(-49/50)(-48/49)(-47/48)*.(-2/3)(-1/2)
There are 49 minus signs in total
=-1/50

Who can teach the process of 1 times 2:1 plus 2 times 3:1 plus 3 times 4:1 plus 49 times 50:1

One by two plus two by three plus three by four plus 49 by 50
=(1-1 / 2) + (1 / 2-1 / 3) + (1 / 3-1 / 4) + (1 / 4-1 / 5) +. + (1 / 49-1 / 50)
=1-1 / 50
=49 out of 50

1 and 2 by 1 and 3 by 1 and 4 by 1.1 and 49 by 1 and 50 by 1
1:2 by 1:3 by 1:4... 1:49 by 1:50

You turn them all into false fractions and they become (3 / 2) * (4 / 3) * (5 / 4) *（50/49）*(51/50)=51/2=25.5
You can't read it like this. You have to read it on paper

Simplification 15:21 0.12:0.4 2 / 7: 1 / 2 / 3 24:42 0.7:0.8

15:21=5:7
0.12:0.4=3:10
2 / 7: 1 / 2 = 4:7
1: Two thirds = 2:3
24:42 =4:7
0.7:0.8=7:8

(- 5 / 6 in 2010) + (- 2 / 3 in 2011) + 4022 + (- 1 / 2), the term splitting method should be used

(- 5 / 6 in 2010) + (- 2 / 3 in 2011) + 4022 + (- 1 / 2)
=-2010-5/6+(-2011-2/3)+4022+(-1-1/2)
=(-2010-2011+4022-1)+(-5/6-2/3-1/2)
=-(5/6+4/6+3/6)
=-12/6
=-2

(- 5 / 6 in 2011) + (- 2 / 3 in 2012) + 4023 + (- 1 / 2) =? Urgent demand ~ ~ (need process)

(- 5 / 6 in 2011) + (- 2 / 3 in 2012) + 4023 + (- 1 / 2)
=（-2011-2012+4023-1）+（-5/6-2/3-1/2）
=-1-2
=-3

1-1 / 2-1 / 6-1 / 12-1 / 20. - 2010 * 2011

1-1 / 2-1 / 6-1 / 12-1 / 20. - 2010 * 2011
=1 - (1 / 2 + 1 / 6 + 1 / 12 +. + 2010 × 1 / 2011)
=1 - (1 / 2 + 1 / 2-3 + 1 / 3-4 +. + 1 / 2010-2011)
=1 - (1 / 1-2011)
=1-1 + 1 / 2011
=1 / 2011

[negative 2012 and 5 / 6] + negative 2011 and 2 / 3] + 4025 + [negative 1 / 2] I want the process and simple calculation. Who can help! Help me!

[negative 2012 and 5 / 6] + [negative 2011 and 2 / 3] + 4025 + [negative 1 / 2]
=(-2012-2011+4025-1)+(-5/6-2/3-1/2)
=1-2
=-1

One half + one sixth + one twelfth, one thirtieth + one fortieth + + 2010 × 2011

One half + one sixth + one twelfth, one thirtieth + one fortieth + + 2010 × 2011
=1-1/2+1/2-1/3+1/3-1/4+.+1/2010-1/2011
=1-1/2011
=2010/2011