Question

Ayuda Por favor no entiendo HALLAR: S=1x11+2x10+3x9+...+11x1 EXPLIQUE ME PORFA

Answer 1

Rescribamos en notación de sumatoria

$\displaystyle\\S=\sum_{i=1}^{11} i(12-i)=\sum_{i=1}^{11}12i-i^2=12\sum_{i=1}^{11}i-\sum_{i=1}^{11}i^2\\ \\ \\S=12\times \dfrac{11(11+1)}{2}-\dfrac{11(11+1)(2\times11+1)}{6}\\ \\ \\S=12\times 11\times 6-11\times 2\times 23\\ \\S=11(72 -46)\\\\S=11(26)\\\\S=286$