Question

600+596+592+......+128+124 suma lui Gauss ​

Answer 1

$600 + 596 + 592 + \dots + 128 + 124 \\ = 4(150 + 149 + \dots+31) \\ = 4 [1 + 2+ \dots + 150 - (1 + 2 + \dots + 30)] \\ = 4( \tfrac{150 \times 151}{2} - \tfrac{30 \times 31}{2} ) \\ = 4 \times( 75 \times 151 - 15 \times 31 )\\ =4\times( 11325 - 465)\\ = 4\times 10860\\ =43440$

Answer 2

$\it S=124+128+132+\ ...\ +600=4(31+32+33+\ ...\ +150)$

Paranteza conține 150-30=120 termeni .

$\it S=4\cdot\dfrac{(31+150)\cdot120}{2}=4\cdot181\cdot60=724\cdot60=43440$