The calculation of the integral formula [(- 2 / 3) to the 8th power multiplied by (3 / 2) to the 8th power] to the 7th power

The calculation of the integral formula [(- 2 / 3) to the 8th power multiplied by (3 / 2) to the 8th power] to the 7th power

[(-2/3)^8*(3/2)^8]^7
=[(-2/3*3/2)^8]^7
=[(-1)^8]^7
=1^7
=1
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Calculate the N + 1 power of 1-2 + 3-4 + 5-6 +... + (- 1) multiplied by n (n is a positive integer), hoping to get a detailed explanation,

When n is even, the result is - N / 2
{the positive number and the number after it, that is, the negative number with an absolute value greater than 1, add to - 1. There are n / 2 - 1 additions}
When n is odd, the result is (n + 1) / 2
{because the sign of this number n is an even power of (- 1), it must be a positive number. There are (n-1) / 2 logarithms in front of N, which add up to (n-1) / 2 - 1, plus N, and the result is n - (n-1) / 2 = (n + 1) / 2}

Calculation: the power of (n + 1) of 1-2 + 3-4 + 5-6 +... (- 1) is multiplied by N, and N is a positive integer

When n is even, the result is - N / 2
{the positive number and the number after it, that is, the negative number with an absolute value greater than 1, add to - 1. There are n / 2 - 1 additions}
When n is odd, the result is (n + 1) / 2
{because the sign of this number n is an even power of (- 1), it must be a positive number. There are (n-1) / 2 logarithms in front of N, which add up to (n-1) / 2 - 1, plus N, and the result is n - (n-1) / 2 = (n + 1) / 2}

Power of X - 5x + 2x-5-x-1 / 3 of 6

=(2x-5)/(x-2)(x-3)-(x-2)/(x-3)(x-2)
=[(2x-5)-(x-2)]/(x-3)(x-2)
=(x-3)/(x-2)(x-3)
=1/(x-3)

(2nd power of X - 2x-3) 1 / 2 + (2nd power of X - X-2) 1 / 2 = (2nd power of X - 5x + 6) 1 / 2

(2nd power of X - 2x-3) 1 / 2 + (2nd power of X - X-2) 1 / 2 = (2nd power of X - 5x + 6) 1 / 2
1/(x+1)(x-3) +1/(x+1)(x-2)=1/(x-2)(x-3)
x-2+x-3=x+1
x=6
Test: x = 6 is the solution of the equation

Judge whether the third power of X + 2x square - 5x-6 can be divided by X + 1

If x in the algebraic formula is a and the algebraic formula = 0, the algebraic formula can be divided by x-a. in this problem, if the algebraic formula = 0 when x = - 1, the algebraic formula can be divided by X + 1. The third power of X + 2x square - 5x-6 = - 1 + 2 + 5-6 = 0. This is the simplest method. Another method is to match x + 1x ^ 3 + 2x ^ 2-5x-6 = (x ^ 3 + x ^ 2