High school math binomial theorem explains in detail

(xy-x-y+1)^n

x-1)^n(y-1)^n

x-1) n after n +1 terms, (y-1) n after n n has n + 1 terms, and there will be no merging of similar terms in the middle of their products.

Its product has (n+1) terms.

n+1）²<=2013

So n min=0 and max=43

Then n=44 is sufficient.

(xy-x-y+1)^n

x-1)^n*(y-1)^n

There should be n+1 terms after x-1) n and n+1 terms after y-1) n.

Multiply the two, and there will be no similar terms.

Thus, there are (n+1) 2 terms in total, and n+1) 2>=2013

n+1>=45

n>=44

So, the minimum value of n is 44

cmk*cn0+cm(k-1)*cn1+cm(k-2)*cn2+……cm0*cnk=c(m+n)k

CMK is m at the bottom and K at the top. Others).

It should be c... A full arrangement,Multiply by 5 is the total time,Subtract the last light of 5 without intervals,It should be the answer.。。。

The permutation of 5 is equal to 120, so there are 119 nulls, and finally it is equal to 120 5 1s + 119 5 = 1195

The coefficient of the coefficient of x in (x-1) is not possible, the coefficient of x in (x-1) is to the power of -c2 2(-1), the coefficient of x in (x-1) is to the power of c3 2(-1), the coefficient of x in -(x-1) 4 is to the power of -c4 2(-1), and the coefficient of x in +(x-1) 5 is to the power of c5 2(-1), so (x-1)-(x-1) +x-1) -x-1) -x-1) 4+(x-1) 5

where the coefficient of x is .

power 0 of c2 2 (-1) + power of 1 of c3 2 (-1) - power of 2 of c4 2 (-1) + power of 3 of c5 2 (-1).

(x-1) 5, which means that there are 5 (x-1) multiplied, and containing x 2 terms means picking out any two x's out of five

Multiply the remaining three (-1) and add all the combinations. There are (5*4) (2*1) possibilities for such a combination, so the x 2 term is equal to (5*4) (2*1)x 2*(-1) 3=-10x 2, so the x2 coefficient is -10

This is a typical method of mathematics, ask your teacher or classmates and ask them to explain it to you carefully.

Then you need to know the Yang Hui triangle, so that you can know the coefficient of x in the equation very quickly.

The sum of the binomial coefficients of (a+b) n is 2 n

The sum of the coefficients is the value of x=1.

But your expression is not very clear, I believe that as long as you understand such a two relationship, you can make it, and if there is any question to me.

(a+b)1= a+b ,a+b)2=a2+2ab+b2

a+b)3=a3+3a2b+3ab2+b3(a+b) 4 = a4+4a3b+6a2b2+4ab3+b4 (here are all in the upper right of the brackets, you should understand, it's not very easy to play here) (a+b)4= (a+b) (a+b) (a+b) (a+b)(a+b)4=c4a4+c4a3b+c4a2b2+c4ab3+c4b4

And so on. Hope it helps.

The formulas of the binomial theorem and the formula for general terms are available in the book.

If you find the nth term, e.g. r+1, substitute r for k.

When finding the constant term, first write the general term formula, then let x=0, get how many k is equal to x=0, and finally substitute k to calculate the constant term.

Finding the middle term: For the middle term of the formula, if n is an even number, then the middle term of the binomial is (n 2)+1 term; If n is an odd number, then there are two intermediate terms in the binomial: (n+1) 2 and (n+1) 2.

Rational term: The rational term in the equation is the term in which the exponent of x in the general term formula is an integer.

Finding the Sum of the Coefficients of the Terms (or Parts) of the Terms: The key to solving the coefficients problem in a polynomial is to assign values to the letters, which can separate the coefficients of the odd (or odd) and even (or even) terms of the polynomial. In general, the sum of the coefficients of the polynomial f(x) is f(1), the sum of the odd coefficients is [f(1)-f(1)], and the sum of the even coefficients is [f(1)+f(1)].

When finding an approximate value, for example, to the power of five, it is required to be accurate. Convert to (2 + power of five again, because it is accurate, so it is not necessary to calculate everything.)

The power of is omitted when the power of the calculation does not play a role in the final exact value even if multiplied by the power of 2 does not play a role in the result of the final exact value. Like this question, the powers of the third, fourth, and fifth powers are omitted.

I also just finished learning, and I remember this. It should work for you. Good luck with O( O

The general term of 5(1) is c(10,r)*(1 2x) r, so that r=5 gives the term containing 1 x 5 is -252 32x 5=-64 8x 5.

2) The general term is c(10,r)*(2x 3) (10-r)*(1 2x 3) r, and when 10-r=r, i.e., r=5, the constant term is -c(10,r)=-252.

8. The conclusion is valid when n=1 and n=2.

n>=3:

n+1)^n-1

c(n,0)n^n+c(n,1)n^(n-1)+c(n,2)n^(n-2)+-c(n,n-1)n+c(n,n)-1

c(n,0)n^n+c(n,1)n^(n-1)+c(n,1)n^(n-1)+-c(n,n-2)n^2+c(n,n-1)n

c(n,0)n^(n-2)+c(n,1)n^(n-3)+-c(n,n-2)+1]*n^2

Divisible by n 2.

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