1.1.3 Evaluate \( \sum_{P=1}^{n} T_{P} \)

To evaluate \( \sum_{P=1}^{n} T_{P} \), we first need to understand what \( T_{P} \) represents. If \( T_{P} \) is a specific term in a sequence defined by some formula, we would need that definition to compute the sum. For instance, if \( T_{P} = P \) (i.e., the sum of the first \( n \) positive integers), then: \[ \sum_{P=1}^{n} T_{P} = \sum_{P=1}^{n} P = \frac{n(n + 1)}{2} \] Alternatively, if \( T_{P} \) follows a different sequence (like \( T_{P} = P^2 \)), then: \[ \sum_{P=1}^{n} T_{P} = \sum_{P=1}^{n} P^2 = \frac{n(n + 1)(2n + 1)}{6} \] Therefore, the evaluation of \( \sum_{P=1}^{n} T_{P} \) depends on the explicit definition of \( T_{P} \). Please clarify the term or sequence for a precise evaluation!