IF `f(r )=1+(1)/(2)+(1)/(3)+"...."+(1)/(r )` and `f(0)=0`, find `sum _(r=1)^(n)(2r+1)f(r )`.

Explanation

To solve the problem, we need to find the sum \( \sum_{r=1}^{n} (2r + 1) f(r) \), where \( f(r) = 1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{r} \) and \( f(0) = 0 \).

### Step-by-Step Solution:

1. **Understanding the Function \( f(r) \)**:
\[ f(r) = \sum_{k=1}^{r} \frac{1}{k} \]
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