`1+3+5+7+9+11+13= (…….)^(2).`

Options

A. `7`
B. `8`
C. `9`
D. `5`

Answer

To solve the equation \(1 + 3 + 5 + 7 + 9 + 11 + 13 = (…….)^2\), we will follow these steps:

### Step 1: Identify the series
The series given is \(1, 3, 5, 7, 9, 11, 13\). This is a series of the first 7 odd numbers.

### Step 2: Count the number of terms
Count the number of terms in the series:
- The terms are: 1, 3, 5, 7, 9, 11, 13
- There are a total of 7 terms.

### Step 3: Use the formula for the sum of the first n odd numbers
The sum of the first \(n\) odd numbers is given by the formula:
\[ \text{Sum} = n^2 \]
where \(n\) is the number of terms.

### Step 4: Calculate the sum
Since we have 7 terms:
\[ \text{Sum} = 7^2 = 49 \]

### Step 5: Write the final equation
Now we can express the original equation as:
\[ 1 + 3 + 5 + 7 + 9 + 11 + 13 = 49 \]
Thus, we can write:
\[ 1 + 3 + 5 + 7 + 9 + 11 + 13 = 7^2 \]

### Final Answer
So, the equation \(1 + 3 + 5 + 7 + 9 + 11 + 13 = (7)^2\).

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