`(1(1)/2+11(1)/2+111(1)/2+1111(1)/2)` is equal to

Options

A. 1236
B. `1234(1)/2`
C. 618
D. 617

Answer

To solve the expression \( (1(1)/2 + 11(1)/2 + 111(1)/2 + 1111(1)/2) \), we can break it down step by step.

### Step 1: Rewrite the expression
The expression can be rewritten as:
\[ \frac{1}{2} + \frac{11}{2} + \frac{111}{2} + \frac{1111}{2} \]

### Step 2: Factor out \(\frac{1}{2}\)
Since \(\frac{1}{2}\) is common in all terms, we can factor it out:
\[ \frac{1}{2} \left( 1 + 11 + 111 + 1111 \right) \]

### Step 3: Calculate the sum inside the parentheses
Now, we need to calculate \( 1 + 11 + 111 + 1111 \):
- \( 1 + 11 = 12 \)
- \( 12 + 111 = 123 \)
- \( 123 + 1111 = 1234 \)

So, we have:
\[ 1 + 11 + 111 + 1111 = 1234 \]

### Step 4: Substitute back into the expression
Now substitute back into the expression:
\[ \frac{1}{2} \times 1234 \]

### Step 5: Multiply to find the final answer
Now, calculate:
\[ \frac{1234}{2} = 617 \]

Thus, the final answer is:
\[ \boxed{617} \]

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