When a shopping mall sells a commodity, its profit margin increases by 8 percentage points because the purchase price is 6.4% lower than the original purchase price?

Let the original purchase price be a yuan, and the original profit rate of this commodity be X. according to the equation, a (1 + x) − a (1 − 6.4%) a (1 − 6.4%) = x + 8%, and the solution is x = 17%

The market will sell a batch of refrigerators at a discount of 75% of the marked price and still make a profit of 25%. If the purchase price is 2100 yuan, what is the marked price of refrigerators

If you get 25% of the marked sales price, the answer is: 2100 / (75% - 25%) = 4200
If you get 25% of the actual sales price, the answer is: 2100 / (1-25%) / 75% = 3733.33
If you get 25% of the purchase price, the answer is: 2100 * (1 + 25%) / 75% = 3500

A certain type of electric heater is sold at the purchase price plus 20%, and the price of each electric heater is 600 yuan. How much is the purchase price of this kind of electric heater?

If the purchase price is set at x yuan, it will be
(1+20%)X=600,
∴X=500,
The purchase price of this electric heater is 500 yuan

If the price of a commodity is 1000 yuan and the purchase price is 600 yuan, how much discount can it sell in order to ensure that the profit is not less than 10%?

Set the minimum discount number as X, according to the meaning of the question: 600 × (1 + 10%) = 1000x, the solution: x = 0.66, that is, you can give a 6.6% discount

The concept of sequence
Given the sequence 1 / 2,2 / 3,3 / 4,4 / 5,..., if the nth term of the sequence is 0.98, find n?

98 = 49 / 50, so n = 49

What is the meaning of dispersion and convergence of sequence?

Dear landlord
In short, convergence is the general term of a sequence. When n tends to infinity, the general term of a sequence tends to a number, that is, there is a limit. I wish you every success

1+3+9+… The sum of the first nine items of the defined sequence is:

1+3+9+27+81+243+729+2187+6561
=9 841
Or A1 = 1, q = 3
Tn= a1(1-q^n)/(1-q)
T9= (1-3^9) /(1-3)=9841

What does it mean that the product of two terms equidistant from the first and last terms is equal,
In a finite equal ratio sequence, the product of two terms equidistant from the first and last terms is equal. In particular, if the number of terms is odd, it is also equal to the square of the middle term. Take an example

The following N, K and m are subscripts
If there is an equal ratio sequence {an}, then an × am = a (n + k) × a (m-k). (m-k ≥ 1, N, m, K ∈ n *)
For example, A1 × A5 = A2 × A4 = A3 × A3
The proof is given below
If an is an equal ratio sequence, then an = A1 × Q ^ (n-1)
an×am=a1×q^（n-1）×a1×q^（m-1）=a1²×q^（m+n-2）.
a（n+k）×a（m-k）=a1×q^（n+k-1）×a1×q^（n-k-1）=a1²×q^（m+n-2）.
Obviously, the two are equal, and the proposition holds

On the concept of sequence boundedness and its limit existence criterion
The criterion for the existence of sequence limit: if the sequence is bounded and monotone, then the limit must exist
But the definition of sequence bounded is not that there is a positive number m, so that the absolute value of sequence xn

If the sequence has a lower bound and monotonically decreasing, the conclusion is that the sequence converges
Easy to understand:
If the sequence is monotonically decreasing, then the first term x [1] is the largest, that is to say, x [1] is its upper bound. If the lower bound n is known, then for any n, there is x [n] between x [1] and N. if the larger number of | x [1] | and | n | is equal to m, then for any n, there is x [n] ≤ M
Generally, the number sequence is monotonically increasing, not to mention the lower bound, because the lower bound is x [1],
Similarly, monotone decreasing does not mean the upper bound, because the upper bound is x [1]

What is the definition of bounded sequence and unbounded sequence? What is the relationship between them?
It's better to give some examples

Definition: if there are two numbers a and B (let A0 be both upper bounds), it means that the upper bound is not unique, and so is the lower bound. (2) for a sequence of numbers, if there is a positive integer n, when n > N, there will always be, we say that the sequence is bounded afterwards

When a shopping mall sells a commodity, its profit margin increases by 8 percentage points because the purchase price is 6.4% lower than the original purchase price?