100 points to find the general term formula, find what is the general term formula for this problem

Answer: an=n!(1-1/1!+1/2!-1/3！+.1)^n*1/n!)

I'll be back in a moment to offer three ideas for proof.

Idea 1: Mathematical induction. There's not much to say about this.

Idea 2: Notice that an a(n-1) is roughly n, let an=n!bn, substitution, got.

bn-b(n-1)=-(b(n-1)-b(n-2))/n, b1=0, b2=1/2.

So, bn-b(n-1)=-(b(n-1)-b(n-2)) n=-(-b(n-2)-b(n-3)) (n-1)) n=....=(-1)^(n-2)(b2-b1)/(n*(n-1)*.3)=(-1)^n*1/n!

So bn=1-1 1!+1/2!-1/3！+.1)^n*1/n!， an=n!bn is equal to the above equation.

Idea 3: This formula is a misplaced arrangement. There is a popular saying about the so-called misplaced arrangement.

n people, each with their own hat. An is the number of times each of them wears the wrong hat. Obviously a1=0 (one cannot wear it wrong), a2=1.

In the case of n>2, the hat of the nth person must be placed on the head of a certain i-person, i=1,2,..n-1, there are two cases of this: 1) if the hat of the ith person is put on the head of the nth person, then the other n-2 people will wear each other incorrectly, and there are a (n-2) ways to wear it;

2) The hat of the other person is put on the head of the nth person, and there are a (n-1) ways to wear it. In summary, we have an=(n-1)(a(n-1)+a(n-2)),n>2And we can use the principle of repulsion to calculate the number of misplaced permutations as above, so there must be an equal to the number above.

1/2!What is it? How do you calculate?

Solve with differential equations, and if it's really 100 points, I'll help you solve it.

In a word: mathematical induction.

But the work has to be hard.

Your recursion: an=(n-1)*a(n-1)+(n-2)*a(n-2) You made a mistake.

The first seventeen are:

Then it overflowed.

General Formula:

The number of a series of eggplants in a certain order is called a number series, and each number in the sequence is called the term of the number, and each item is called the first term (or the first term), the second term, and all the way up to the nth term. A sequence can also be thought of as a function that defines the domain as a natural set of numbers n (or a finite subset of it), and the corresponding column of function values when the independent variables take their values from smallest to largest.

Properties: 1. If the general formula of a series of numbers is known, then as long as it is replaced by n in the formula in turn, the terms of the series can be found.

2. Not every infinite number series has a general term formula, for example, all the numbers composed of prime numbers do not have a general term formula.

3. The first n terms of the series are given, and the formula for the general terms is not unique.

4. The general term of some sequences can be expressed by two or more formulas.

The general formulas include equal difference series, proportional series, first-order series, second-order series, accumulation method, cumulative multiplication method, construction method, such as the royal addition and subtraction method. A series of numbers arranged in a certain order is called a sequence, and the nth term of a series is expressed by a specific formula (containing parameter n), which is called the general term formula of the series.

This is like the analytic expression of a function, which can be found by substituting the specific n value to find the value of the corresponding an term. The method of finding the general term formula of the number series is usually obtained by the recursive formula of the slag wheel rock through several transformations.

That's what I thought.

sn=1/5an-1/5

s(n-1)=1/5a(n-1)-1/5

Subtraction. Cavity oak an=1 5an-1 5a(n-1)an rent Yuanxiao a(n-1)=-1 4=common ratio, so it is a proportional series.

a1=5a1+1 ==a1=-1/4

so ,an=(-1/4)^n

Fibonacci sequence fn

The general formula an=f(n+2) f(n+1).

The first question is A, Analysis: Use a n+1 a nWhen n = 2 or 3 is the smallest, 8 9, it can also be seen that the number series is an increasing series at n 2 and a decreasing series at n 3.