The formula I = nqvs is used to explain the physical constant current

The formula I = nqvs is used to explain the physical constant current

Let the number of free charges per unit volume in a conductor be n, the cross-sectional area of the conductor be s, the electric quantity of the free charge be q, and the directional moving velocity of the free charge be v,
Taking any cross section in the conductor, it is obvious that the charge passing through the cross section in time t must be in a cylinder with the cross section as the bottom and V * t as the length
The volume of the cylinder V '= s * V * t (1)
The number of charges contained is: n = n * V '(2)
Q = n * q (3)
So the current is I = q / T (4)
Replace formula 1.2.3 with formula (4) to get: I = nqvs

How to solve the formula of 4.1 + (- 2) + 3 + (- 4) +. + 99 + (- 100)! We have to wait tomorrow!

1+(-2)+3+(-4)+.+99+(-100)
=-1*(100/2)
=-1*50
=-50

High school mathematics compulsory 5 series of a problem ~ some places do not understand, I hope you can help solve it
The sum of the first n terms of sequence 1, 1 + 2, 1 + 2 + 2 ^ 2,. 1 + 2 + 2 ^ 2 + 2 ^ 3 +... + 2 ^ n-1 is equal to?
I read the answer, there is a place I don't quite understand. Through the above sequence, I can use sn-sn-1 to find an = (1-2 ^ n) / (1-2) = 2 ^ n - 1, and then I can't understand it. It says Sn = 2 (1-2 ^ n) / (1-2) - n = 2 ^ n + 1-N - 2 (final result). Why should the SN = 2 (1-2 ^ n) / (1-2) - n be reduced by N? What's the meaning? And why Sn = 2 (1-2 ^ n) / (1-2) - N? Hope the master can give a detailed answer, thank you~~~~

An = (1-2 ^ n) / (1-2) = 2 ^ n - 1 here you can understand
So Sn = a1 + A2 +... + an = (2-1) + (2 ^ 2-1) + (2 ^ 3-1) + (2 ^ n-1) = (2 + 2 ^ 2 + 2 ^ 3 +. + 2 ^ n) - n
Because each term has to subtract a 1, the first n terms have n 1, so subtract n
Then we can get Sn = 2 (1-2 ^ n) / (1-2) - n = 2 (2 ^ n-1) - N by using the sum formula of the first n terms of the equal ratio sequence