125

361

15-6 = 9

Ta có: \(C = 1 \cdot 3 + 2 \cdot 4 + 3 \cdot 5 + \hdots + 49 \cdot 51\)

\(= 1 \left(\right. 1 + 2 \left.\right) + 2 \left(\right. 2 + 2 \left.\right) + \hdots + 49 \left(\right. 49 + 2 \left.\right)\)

\(= \left(\right. 1^{2} + 2^{2} + \hdots + 4 9^{2} \left.\right) + 2 \left(\right. 1 + 2 + \hdots + 49 \left.\right)\)

\(= \frac{49 \left(\right. 49 + 1 \left.\right) \left(\right. 2 \cdot 49 + 1 \left.\right)}{6} + 2 \cdot \frac{49 \cdot 50}{2} = \frac{49 \cdot 50 \cdot 99}{6} + 49 \cdot 50\)

\(= 49 \cdot 25 \cdot 33 + 49 \cdot 50 = 49 \cdot 25 \left(\right. 33 + 2 \left.\right) = 49 \cdot 25 \cdot 35 = 42875\)

ez 210