`1+(1)/(2)+(1)/(4)+(1)/(7)+(1)/(14)+(1)/(28)` is equal to:

Options

A. 2
B. 2.5
C. 3
D. 3.5

Answer

To solve the expression \( 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{7} + \frac{1}{14} + \frac{1}{28} \), we will follow these steps:

### Step 1: Identify the denominators
The denominators in the expression are \( 1, 2, 4, 7, 14, \) and \( 28 \).

### Step 2: Find the Least Common Multiple (LCM)
To add these fractions, we need a common denominator. The LCM of \( 1, 2, 4, 7, 14, \) and \( 28 \) is \( 28 \).

### Step 3: Rewrite each term with the common denominator
Now, we will rewrite each fraction with \( 28 \) as the denominator:
- \( 1 = \frac{28}{28} \)
- \( \frac{1}{2} = \frac{14}{28} \)
- \( \frac{1}{4} = \frac{7}{28} \)
- \( \frac{1}{7} = \frac{4}{28} \)
- \( \frac{1}{14} = \frac{2}{28} \)
- \( \frac{1}{28} = \frac{1}{28} \)

### Step 4: Combine the fractions
Now we can add all the fractions together:
\[ \frac{28}{28} + \frac{14}{28} + \frac{7}{28} + \frac{4}{28} + \frac{2}{28} + \frac{1}{28} = \frac{28 + 14 + 7 + 4 + 2 + 1}{28} \]

### Step 5: Calculate the numerator
Now, let's calculate the sum of the numerators:
\[ 28 + 14 + 7 + 4 + 2 + 1 = 56 \]

### Step 6: Write the final fraction
So, we have:
\[ \frac{56}{28} \]

### Step 7: Simplify the fraction
Now we can simplify \( \frac{56}{28} \):
\[ \frac{56}{28} = 2 \]

### Final Answer
Thus, the value of \( 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{7} + \frac{1}{14} + \frac{1}{28} \) is \( 2 \).

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