Calculate :
`1-2+3-4+5-6+7-8+9-10`

Answer

To solve the expression \(1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 - 10\), we can group the terms in pairs to make the calculation easier. Here’s a step-by-step solution:

### Step 1: Group the terms
We can group the terms as follows:
\[ (1 - 2) + (3 - 4) + (5 - 6) + (7 - 8) + (9 - 10) \]

### Step 2: Calculate each group
Now, we will calculate each group:
- For the first group:
\[ 1 - 2 = -1 \]
- For the second group:
\[ 3 - 4 = -1 \]
- For the third group:
\[ 5 - 6 = -1 \]
- For the fourth group:
\[ 7 - 8 = -1 \]
- For the fifth group:
\[ 9 - 10 = -1 \]

### Step 3: Add the results of the groups
Now we add all the results from the groups:
\[ -1 + (-1) + (-1) + (-1) + (-1) \]

### Step 4: Simplify the addition
Adding these together gives:
\[ -1 - 1 - 1 - 1 - 1 = -5 \]

### Final Answer
Thus, the final result of the expression \(1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 - 10\) is:
\[ \boxed{-5} \]