`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 the fractions, we need a common denominator. The LCM of the denominators (2, 4, 7, 14, and 28) is 28.

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

### 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, we 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 simplify \( \frac{56}{28} \):
\[ \frac{56}{28} = 2 \]

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