Calculate: `1-2+3-4+5-6+...+15-16`

Answer

To solve the expression `1 - 2 + 3 - 4 + 5 - 6 + ... + 15 - 16`, we can follow these steps:

### Step 1: Identify the Pattern
The expression consists of alternating addition and subtraction of consecutive integers from 1 to 16. We can group the terms in pairs:
- (1 - 2)
- (3 - 4)
- (5 - 6)
- (7 - 8)
- (9 - 10)
- (11 - 12)
- (13 - 14)
- (15 - 16)

### Step 2: Calculate Each Pair
Now, let's calculate each pair:
- 1 - 2 = -1
- 3 - 4 = -1
- 5 - 6 = -1
- 7 - 8 = -1
- 9 - 10 = -1
- 11 - 12 = -1
- 13 - 14 = -1
- 15 - 16 = -1

Each pair results in -1.

### Step 3: Count the Number of Pairs
From 1 to 16, we have a total of 16 numbers. Since we are pairing them, we have:
- Total pairs = 16 / 2 = 8 pairs.

### Step 4: Sum the Results of the Pairs
Since each pair sums to -1 and there are 8 pairs:
- Total = 8 * (-1) = -8.

### Final Answer
Thus, the value of the expression `1 - 2 + 3 - 4 + 5 - 6 + ... + 15 - 16` is **-8**.

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