How do these numbers find the rule 1, 2, 4, 8, 16, 32 Up to 64, how much does it add up to? What is the rule formula?

How do these numbers find the rule 1, 2, 4, 8, 16, 32 Up to 64, how much does it add up to? What is the rule formula?

The law is an n-1 power of an = 2
And Sn = A1 (1-Q ^ n) / (1-Q)

A three digit natural number is exactly 18 times the sum of its digits______ .

Let this natural number be ABC
100A+10B+C=18（A+B+C）
After simplification, 82a = 8b + 17c
Because B and C are 9 at most, 82a is 8 × 9 + 17 × 9 = 225, that is, a can only be 1 or 2
When a = 1, we get 82 = 8b + 17c, from B, C are integers less than 9, we can get: B = 6, C = 2;
When a = 2, 164 = 8b + 17c, B = 12, C = 4 (round off)
So this three digit number is 162
So the answer is: 162

What is the common meaning of the 7 numbers that do not repeat?

（36*35*34*33*32*31*30） / （7*6*5*4*3*2*1）= 8347680

A formula for calculating the probability times of a group of disordered numbers For example: 1 2 3 4 5 6 7 8 What is the probability and frequency of occurrence of three numbers in a group?

Times: P3 (superscript) 8 (subscript) = 6 × 7 × 8 = 336
Any three of the eight numbers: C3 (superscript) 8 (subscript);
The three numbers are disordered: P3 (superscript) 3 (subscript);
The number of times is the sum of times
Probability: now calculate the total number of times: (algorithm as above)
A number is the number of times a group appears, C1 (superscript) 8 (subscript) × P1 (superscript) 1 (subscript),
Two numbers are the number of times a group appears, C2 (superscript) 8 (subscript) × P2 (superscript) 2 (subscript),
Three numbers are the number of times a group appears, C3 (superscript) 8 (subscript) × P3 (superscript) 3 (subscript),
…… …… …… …… ,…… …… …… …… …… ,
Eight numbers are the number of times a group appears, C8 (superscript) 8 (subscript) × P8 (superscript) 8 (subscript);
[Note: CX (superscript) 8 (subscript) × PX (superscript) x (subscript) = PX (superscript) 8 (subscript);]
This is a big number. Take your time. The total number is 109600
Then the probability is 336 / 109600 = 21 / 6850 = 0.003

Formula of combination number Let C (5,3) C (5,3) = (5 * 4 * 3) / 6 = 30 The value of C (5,3) = 120 / (6 * 2) = 10 I don't think so

Pro! 5 * 4 * 3 / 6 = 10

What is the formula of combinatorial number?

C-n-m (subscript n, superscript m) = n! Divided by [M! Times (n-m)!]

On the formula of combinatorial number c(n,1)+2c(n,2)+...+nc(n,n) = n[c(n-1,0)+c(n-1,1)+...+c(n-1,n-1)]=n2^n-1

Let Sn = C (n, 1) + 2C (n, 2) +... + NC (n, n) -- (1)
c(n,m)=c(n,n-m)
Write Sn backwards
Sn=nc(n,n)+(n-1)c(n,n-1)+...2c(n,2)+c(n,1)---(2)
(1) + 2
2Sn=n(c(n,0)+c(n,1)+...c(n,n-1)+c(n,n))=n*2^n
Sn=n*2^n-1

The formula of combination number

nPm=n(n-1)(n-2)(n-3).(n-m+1)
nPn=n!,0!=1
nCm=nPm/mPm=n!/[m!(n-m)!]
nPm=n*(n-1)P(m-1)
nCm=nC(n-m)
(n+1)Cm=nC(m-1)+nCm
nC0+nC1+nC2+.+nCn=2^n
k*nCk=n*(n-1)C(k-1)
nC0*nCn+nC1*nC(n-1)+...+nCn*nC0
=nC0*nC0+nC1*nC1+.+nCn*nCn=(2n)Cn
kCk+(k+1)Ck+(k+2)Ck+...+nCk=(n+1)C(k+1)

What is the permutation number formula?

That sign is not easy to write. Use this a (n, m) instead. N and m are subscripts and superscripts respectively
A(n,m)=n(n-1)(n-2)…… (n-m+1)= n!/(n-m)!

How many ways to arrange the numbers? 1. If you toss a coin three times in a row, what is the probability of the positive and negative alternating? 2. If you take two different numbers from 1, 2, 3, 4 and 5 to form a two digit number, calculate the probability that the two digits are greater than 40. Please explain it to the intellectuals,

1. If the first time is the front, then the probability is 50% * 50% * 50%. The first time is the back, so the probability is
2*50%*50%*50%=25%
2. If two digits are greater than 40, then the value of ten digits may be
When 4,5 tens are correct, there is no limit on the value of single digit
So the probability of probability greater than 40 is 2 / 5 = 40%