A few junior one's, on the absolute value of the formula, requires simple calculation I can't get the score, for example, half is expressed as 1 / 2 Question 1: 1 / 1001-1 / 100 + 1 / 1002-1 / 1001 - 1 / 1002-1 / 1000 Question 2: 1 / 2-1 / 3 + 1 / 3-1 / 4 + 1 / 4-1 / 5 + 1 / 49-1 / 50 Ask for a brief calculation and list the steps

A few junior one's, on the absolute value of the formula, requires simple calculation I can't get the score, for example, half is expressed as 1 / 2 Question 1: 1 / 1001-1 / 100 + 1 / 1002-1 / 1001 - 1 / 1002-1 / 1000 Question 2: 1 / 2-1 / 3 + 1 / 3-1 / 4 + 1 / 4-1 / 5 + 1 / 49-1 / 50 Ask for a brief calculation and list the steps

1. Original formula = - (1 / 1001-1 / 1000) - (1 / 1002-1 / 1001) + (1 / 1002-1 / 1000)
=1/100+(1/1001-1/1001)+1/1002-1/1002-1/1000
=1/1000-1/1000
=0
2. The original formula is 1 / 2-1 / 3 + 1 / 3-1 / 4 + 1 / 4-1 / 5 +. + 1 / 48-1 / 49 + 1 / 49-1 / 50
=1/2-1/50
=12/25
That's the way to do it. I have to doubt if it's so simple. In fact, it's to remove the absolute value from the above question. If the number in front of the absolute value is less than the number in the back, it's necessary to add symbols, and the following one doesn't need to feel. Is the following one more simple? You need to train more. It's more complicated in high school. And that's 1 / 1000