`s lambda t=(t)/(s)+(s)/(t)` for all inntegers s ant t. What is the value of `2lambda16`?

Answer

To solve the problem \( 2 \lambda 16 \) using the defined operation \( s \lambda t = \frac{t}{s} + \frac{s}{t} \), we will follow these steps:

### Step 1: Identify the values of \( s \) and \( t \)
From the expression \( 2 \lambda 16 \), we can identify:
- \( s = 2 \)
- \( t = 16 \)

### Step 2: Substitute \( s \) and \( t \) into the operation definition
Now, we substitute these values into the operation definition:
\[ 2 \lambda 16 = \frac{16}{2} + \frac{2}{16} \]

### Step 3: Calculate each term
Now we calculate each term separately:
1. Calculate \( \frac{16}{2} \):
\[ \frac{16}{2} = 8 \]
2. Calculate \( \frac{2}{16} \):
\[ \frac{2}{16} = \frac{1}{8} \]

### Step 4: Add the results
Now we add the two results together:
\[ 2 \lambda 16 = 8 + \frac{1}{8} \]

### Step 5: Convert to a mixed number
To express \( 8 + \frac{1}{8} \) as a mixed number:
\[ 8 + \frac{1}{8} = 8 \frac{1}{8} \]

### Final Answer
Thus, the value of \( 2 \lambda 16 \) is:
\[ \boxed{8 \frac{1}{8}} \]