The value of `(1+(1)/(2)) (1+(1)/(3))(1+(1)/(4))....(1+(1)/(120))` is

Options

A. 30
B. `40.5`
C. `60.5`
D. `121`

Answer

To solve the expression \((1 + \frac{1}{2})(1 + \frac{1}{3})(1 + \frac{1}{4}) \ldots (1 + \frac{1}{120})\), we will follow these steps:

### Step 1: Rewrite Each Term
Each term in the product can be rewritten as:
\[ 1 + \frac{1}{n} = \frac{n + 1}{n} \]
Thus, we can rewrite the entire expression as:
\[ (1 + \frac{1}{2})(1 + \frac{1}{3})(1 + \frac{1}{4}) \ldots (1 + \frac{1}{120}) = \frac{3}{2} \cdot \frac{4}{3} \cdot \frac{5}{4} \cdots \frac{121}{120} \]

### Step 2: Write the Product
Now, we can express the product more clearly:
\[ = \frac{3 \cdot 4 \cdot 5 \cdots \cdot 121}{2 \cdot 3 \cdot 4 \cdots \cdot 120} \]

### Step 3: Simplify the Product
Notice that in the numerator and denominator, many terms will cancel out:
- The \(3\) in the numerator cancels with the \(3\) in the denominator.
- The \(4\) in the numerator cancels with the \(4\) in the denominator.
- This pattern continues up to \(120\).

After cancellation, we are left with:
\[ = \frac{121}{2} \]

### Step 4: Calculate the Final Value
Now, we can compute the final value:
\[ \frac{121}{2} = 60.5 \]

### Final Answer
Thus, the value of the expression \((1 + \frac{1}{2})(1 + \frac{1}{3})(1 + \frac{1}{4}) \ldots (1 + \frac{1}{120})\) is:
\[ \boxed{60.5} \]