Question

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Answer 1

To evaluate the series \(99 - 97 + 95 - 93 + \dots + 3 - 1\), let's break it down step-by-step.

### **Step 1: Identify the Pattern**
The series alternates between adding and subtracting consecutive odd numbers, starting from 99 and ending at 1:
\[
99 - 97 + 95 - 93 + \dots + 3 - 1
\]

### **Step 2: Determine the Number of Terms**
First, count how many odd numbers are there from 99 down to 1.

- The sequence of odd numbers from 1 to 99 is: \(1, 3, 5, \dots, 99\).
- The \(n\)-th odd number is given by \(2n - 1\).
- To find the number of terms (\(n\)) when the last term is 99:
\[
2n - 1 = 99 \implies 2n = 100 \implies n = 50
\]
So, there are **50 terms** in total.

### **Step 3: Group the Terms**
The series alternates between addition and subtraction. Group the terms in pairs:
\[
(99 - 97) + (95 - 93) + \dots + (3 - 1)
\]
Each pair simplifies to:
\[
99 - 97 = 2, \quad 95 - 93 = 2, \quad \dots, \quad 3 - 1 = 2
\]

### **Step 4: Count the Number of Pairs**
Since there are 50 terms in total, and each pair consists of 2 terms, the number of pairs is:
\[
\frac{50}{2} = 25 \text{ pairs}
\]

### **Step 5: Calculate the Total Sum**
Each pair sums to 2, and there are 25 such pairs:
\[
\text{Total Sum} = 25 \times 2 = 50
\]

### **Final Answer**
\[
\boxed{50}
\]

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Answer 2

To evaluate the series \(99 - 97 + 95 - 93 + \dots + 3 - 1\), let's break it down step-by-step.

### **Step 1: Identify the Pattern**
The series alternates between adding and subtracting consecutive odd numbers, starting from 99 and ending at 1:
\[
99 - 97 + 95 - 93 + \dots + 3 - 1
\]

### **Step 2: Determine the Number of Terms**
First, count how many odd numbers are there from 99 down to 1.

- The sequence of odd numbers from 1 to 99 is: \(1, 3, 5, \dots, 99\).
- The \(n\)-th odd number is given by \(2n - 1\).
- To find the number of terms (\(n\)) when the last term is 99:
\[
2n - 1 = 99 \implies 2n = 100 \implies n = 50
\]
So, there are **50 terms** in total.

### **Step 3: Group the Terms**
The series alternates between addition and subtraction. Group the terms in pairs:
\[
(99 - 97) + (95 - 93) + \dots + (3 - 1)
\]
Each pair simplifies to:
\[
99 - 97 = 2, \quad 95 - 93 = 2, \quad \dots, \quad 3 - 1 = 2
\]

### **Step 4: Count the Number of Pairs**
Since there are 50 terms in total, and each pair consists of 2 terms, the number of pairs is:
\[
\frac{50}{2} = 25 \text{ pairs}
\]

### **Step 5: Calculate the Total Sum**
Each pair sums to 2, and there are 25 such pairs:
\[
\text{Total Sum} = 25 \times 2 = 50
\]

### **Final Answer**
\[
\boxed{50}
\]

Answer 3

Campuchia đấy

Số thứ tự	Loại hàng	Số lượng (quyển)	Giá đơn vị (đồng)	Tổng số tiền (đồng)
1	Vở loại 1	35	2000	...
2	Vở loại 2	42	1500	...
3	Vở loại 3	38	1200	...
Cộng:				...

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