If `{x}` and `[x]` represent fractional and integral part of x respectively, find the value of `[x]+sum_(r=1)^(2000)({x+r})/2000`

Explanation

To solve the problem, we need to find the value of \([x] + \frac{\sum_{r=1}^{2000} \{x + r\}}{2000}\), where \([x]\) is the integral part of \(x\) and \(\{x\}\) is the fractional part of \(x\).

### Step-by-Step Solution:

1. **Understanding the Components**:
- Let \([x] = n\) (the integral part of \(x\)).
- Let \(\{x\} = f\) (the fractional part of \(x\)).
- Thus, we can express \(x\) as:
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