Question

SERIES Y SUMATORIAS.- Calcular la siguiente suma:

Answer 1

Respuesta:

Alternativa B) 84 575

Explicación paso a paso:

Hola espero que entiendas ✌️

$a(n - a) = an - {a}^{2}$

$s = 1 \times 99 + 2 \times 98 + 3 \times 97 + ... + 50 \times 50 \\ s = 1 \times (100 - 1) + 2 \times (100 - 2) + 3 \times (100 - 3) + ... + 50 \times (100 - 50) \\ s = 1 \times 100 - {1}^{2} + 2 \times 100 - {2}^{2} + 3 \times 100 - {3}^{2} + ... + 50 \times 100 - {50}^{2} \\ s = 100 \times (1 + 2 + 3 + ... + 50) - ( {1}^{2} + {2}^{2} + {3}^{2} + ... + {50}^{2} ) \\ s = 100 \times ( \frac{50}{2} \times (1 + 50)) - \frac{50 \times (50 + 1) \times (2 \times 50 + 1)}{6} \\ s = 50 \times 50 \times 51 - \frac{25 \times 51 \times 101}{3} \\ s = {50}^{2} \times 51 - 25 \times 17 \times 101 \\ s = 127500 - 42925 \\s = 84575$