What is one plus two plus three plus four plus five all the way to 100 Add with the beginning and end

What is one plus two plus three plus four plus five all the way to 100 Add with the beginning and end

(1+100)×（100÷2）
=101×50
=5050

When calculating the value of 1 + 3 + 3's quadratic + ·· + 3's 100th power, let s = 1 + 3 + 3's quadratic + ·· + 3's 100th power, then 3S = 3 + 3's quadratic
The 101st power of the third power + ·· + 3 is 2,2-1, and the 101st power of 2S = 3 is - 1, so the 101st power of S = 3 / 2 is - 1. Try to use the above method to find the value of the quadratic power of 1 + 8 + 8 + ·· + 8 to the power of 2004, and find the value of the quadratic power of 1 + X + X + · + X to the power of n (x is not equal to 1)

Let s = 1 + 8 + 8 to the second power + ·· + 8 to the fourth power
Then 8s = quadratic power of 8 + 8 + 8 + ·· + 2004 power of 8 + 2005 power of 8
By subtracting the two formulas, we get: 8s-s = 8 to the power of 2005-1
S = 1 / 7 (power of 8-1)
Let s = 1 + X + X to the second power + ·· + X to the nth power
Then XS = quadratic power of X + X + ·· + n power of X + N + 1 power of X
By subtracting the two formulas, we get the following result:
(x-1) s = n + 1 power-1 of X
S = (n + 1 power of x-1) / (x-1)

1 / 3-1 / 3-1 / 3-1 / 3 of the square - 1 / 3 to the 100th power

The square of 1-1 / 3-1 / 3 is the third power of 1 / 3 - 1 / 3 to the power of 100;
1 / 3 + the square of 1 / 3 + the third power of 1 / 3 +1 / 3 to the 100th power = a;
3A = the square of 1 + 1 / 3 + 1 / 3 + the third power of 1 / 3 +1 / 3 to the power of 99;
2A = 100th power of 1-1 / 3;
The square of 1-1 / 3-1 / 3 is the third power of 1 / 3 - 1 / 3 to the 100th power
=1 - (100th power of 1-1 / 3) / 2
=(100th power of 1 + 1 / 3) / 2