Teach me a math problem 1 + 2 + 3 +. + 100 =?

Teach me a math problem 1 + 2 + 3 +. + 100 =?

1+2+3+.+100
=(1+100)*100/2
=5050

1/(a-1)+1/(a-1)(a-2)+1(a-2)(a-3).1/(a-99)(a-100)

1/(a-1)+1/(a-1)(a-2)+1(a-2)(a-3).1/(a-99)(a-100)
=1/(a-1)+1/(a-1)-1/(a-2)+1/(a-2)-1/(a-3)+.+1/(a-99)-1/(a-100)
=2/(a-1)-1/(a-100)
=[2(a-100)-2]/(a-1)(a-100)
=(2a-202)/(a-1)(a-100)

8000-1-2-3-4... - 87-88-99-100 a math problem

8000-1-2-3-4.．．．-87-88-99-100
=8000-(1+2+3．．．+100)
=8000-(1+100)*100/2
=8000-(1+100)*100/2
=8000-5050
=2950

Ask a math problem: (- 1) + 2 + (- 3) + 4 + (- 5) + 6 +... + (- 99) + 100

The former and the latter two numbers add up to 1, like (- 1) + 2 = 1, (- 3) + 4 = 1, two numbers are a group, there are 100 numbers, there are 100 / 2 groups, that is 50 groups, the original formula is that 50 ones add up, that is 50