Math Problem 3 Ask 20 with high fingers

Method 1: Forcibly a(n) expression

1+2+……n=n(n+1)/2

1^2+2^2+……n^2=n(n+1)(2n+1)/6

1^3+2^3+……n^3=n^2(n+1)^2/4

1^4+2^4+……n 4 = n (15n 3 + 10n 2-1) 30, and then substitute into the formula a(n) = n (n + 1) (n + 2) (n + 3), a(n) after a(n) = 5 (n 4 + 6n 3 + 11n 2 + 6n), and then substitute into the operation.

Method 2: Matching method].

Because an=(1 5)[n(n+1)(n+2)(n+3)(n+4)-(n-1)n(n+1)(n+2)(n+3)].

Let n = 1,2 ,......n got.

a1=(1/5)(1*2*3*4*5)

a2=(1/5)(2*3*4*5*6-1*2*3*4*5)

a3=(1/5)(3*4*5*6*7-2*3*4*5*6)

an=(1/5)[n(n+1)(n+2)(n+3)(n+4)-(n-1)n(n+1)(n+2)(n+3)]

The above n formulas are added together.

sn=n(n+1)(n+2)(n+3)(n+4)/5

Method 3: Combinatorial Number Operation].

When you see n(n+1)(n+2)(n+3), you remember that it is part of factorial.

a(n)/4!=n(n+1)(n+2)(n+3)/4!

Number of combinations (n+3,4).

n+4,5)-(n+3,5)

s(n)/4!-s(n-1)/4!

Therefore, s(n)=(n+4,5)*4!

n(n+1)(n+2)(n+3)(n+4)/5

Method 4: Split term method].

a(n)-a(n-1)=4n(n+1)(n+2)

a(n-1)-a(n-2)=4(n-1)n(n-2)

a2-a1=4*2*3*4

a1 =4*3*2*1

Summing yields a(n)=4n(n+1)(n+2).

From this, we can let b(n)=5n(n+1)(n+2)(n+3).

Similarly: sn=n(n+1)(n+2)(n+3) 5

82 78

The product of two numbers is 6396, and the first tens must be 9 or 8, and 92 is not divisible, so it is 82

82*78=6396

The first blank fills 8, and the second fills 8

The landlord can calculate whether it is right or not.

It's 8, set the answer with a calculator.

The process is not good to write, I don't know how to use mathematical notation, the answer is.

aeoh+cgof=bfoe+dhog, so s quadrilateral dhog=5 aoe and boe are equal in height, so s oaes obe can be proved in the same way, s obf

s△ocfs△odg

s△ocgs△odh

s△oah

Connect OA, OB, OC, OD

Since EFGH is the midpoint of the four edges, S oae = S obe (the bottom edge, the height is equal) Let the area be a

Similarly, let s obf=s ocf=b,s ocg=s odg=c,s odh=s oah=d

then S oah+s oae=a+d=4 (1)s obe+s obf=a+b=5 (2)s oBF+s oG=b+c=6 (3)1)+(3)-(2)=(a+d) +b+c) -a+b)=c+d=4+6-5=5

s quadrilateral dhog=s odg+s odh=c+d=5

Set the passenger car speed is 7a, the truck speed is 5a, 7a-5a = 5000, a = 2500, the truck speed is 5a = 125000, the total length is 4 (7 + 5) a = 120000It takes 120,000 12,500 = hours for a truck to get from B to A.

If the speed of the passenger car is 7x, the speed of the truck is 5x

7x-5x=5

x = that is, the speed of the passenger car is 7*, and the speed of the truck is 5*km/h.

ab distance: 4*(km.)