Question

De calculat. Multumesc

Answer 1

Răspuns:

40

Explicație pas cu pas:

${1}^{2} - {2}^{2} - {3}^{2} + {4}^{2} + {5}^{2} - {6}^{2} - {7}^{2} + {8}^{2} + ... + {37}^{2} - {38}^{2} - {39}^{2} + {40}^{2} = ({1}^{2} - {2}^{2}) - ({3}^{2} - {4}^{2}) + ({5}^{2} - {6}^{2}) - ({7}^{2} - {8}^{2}) + ... + ({37}^{2} - {38}^{2}) - ({39}^{2} - {40}^{2}) = (1 - 2)(1 + 2) - (3 - 4)(3 + 4) + (5 - 6)(5 + 6) - (7 - 8)(7 + 8) + ... + (37 - 38)(37 + 38) - (39 - 40)(39 + 40) = - 1 \times 3 + 1 \times 7 - 1 \times 11 + 1 \times 15 + ... - 1 \times 75 + 1 + 79 = ( - 3 + 7) + ( - 11 + 15) + ... + ( - 75 + 79) = 4 + 4 + ... + 4 = 4×10=40$