Question

Calcula el valor de la serie:A = 1 + 1 + 4 + 8 + 9 + 27 + ... + 100 + 1000

Answer 1

Respuesta:

A = 3410

Explicación paso a paso:

A = 1 + 1 + 4 + 8 + 9 + 27 + ... + 100 + 1000

A =

${1}^{2} + {1}^{3} + {2}^{2} + {2}^{3} + {3}^{2} + {3}^{3} + ... + {10}^{2} + {10}^{3}$

A =

${1}^{2} + {2}^{2} + {3}^{2} + ... + {10}^{2} + {1}^{3} + {2}^{3} + {3}^{3} + ... + {10}^{3}$

A =

$\frac{(10 \times 11 \times 21)}{6} + ({ \frac{10 \times 11}{2} })^{2} \\ \frac{2310}{6} + ({ \frac{110}{2} })^{2} \\ 385 + {55}^{2} \\ 385 + 3025 \\ 3410$