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

Options

A. 2.5
B. 2
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 \(1, 2, 4, 7, 14, 28\). The least common multiple (LCM) of these numbers will help us combine the fractions.

### Step 2: Find the LCM
The LCM of \(2, 4, 7, 14, 28\) is \(28\). Thus, we will convert each term to have a denominator of \(28\).

### Step 3: Convert each term to have a common denominator
- \(1 = \frac{28}{28}\)
- \(\frac{1}{2} = \frac{14}{28}\) (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: Rewrite the expression
Now, we can rewrite the expression as:
\[ \frac{28}{28} + \frac{14}{28} + \frac{7}{28} + \frac{4}{28} + \frac{2}{28} + \frac{1}{28} \]

### Step 5: Combine the fractions
Now, we can combine the numerators:
\[ \frac{28 + 14 + 7 + 4 + 2 + 1}{28} = \frac{56}{28} \]

### Step 6: Simplify the fraction
Now, 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 \(2\).

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