Find the value of
`[3/4]+[3/4+1/100]+[3/4+2/100]+...+[3/4+99/100]`.

Answer

To solve the problem, we need to find the value of the expression:

\[ [3/4] + [3/4 + 1/100] + [3/4 + 2/100] + \ldots + [3/4 + 99/100] \]

### Step-by-Step Solution:

1. **Identify the first term:**
The first term is \([3/4]\). The floor function \([x]\) gives the greatest integer less than or equal to \(x\). Since \(3/4 = 0.75\), we have:
\[ [3/4] = 0 \]

2. **Calculate the subsequent terms:**
The terms can be expressed as:
\[ [3/4 + k/100] \quad \text{for } k = 0, 1, 2, \ldots, 99 \]
We can rewrite this as:
\[ [0.75 + k/100] \]

3. **Determine when the floor function changes:**
The value of \(0.75 + k/100\) will be less than 1 when \(k < 25\) (since \(0.75 + 0.25 = 1\)). Therefore:
- For \(k = 0\) to \(k = 24\):
\[ [0.75 + k/100] = 0 \]
- For \(k = 25\) to \(k = 99\):
\[ [0.75 + k/100] = 1 \]

4. **Count the number of terms:**
- There are \(25\) terms where \(k = 0\) to \(k = 24\) contributing \(0\).
- There are \(75\) terms where \(k = 25\) to \(k = 99\) contributing \(1\).

5. **Calculate the total sum:**
The total sum can be calculated as:
\[ \text{Total Sum} = 0 \times 25 + 1 \times 75 = 0 + 75 = 75 \]

### Final Answer:
Thus, the value of the expression is:
\[ \boxed{75} \]