Question

14. Comparați numerele a şi b, date de: 2-(64-1)-(64-2²)-(64-3²)... (64-10²); b- (1¹-64) (2¹-64) (3¹-64)... (10-64)
va rog ajutati-ma! Dau coroana​

Answer 1

$a = 2 - (64 - 1) - (64 - {2}^{2}) - (64 - {3}^{2}) - ... - (64 - {10}^{2}) = 2 - 64 + 1 - 64 + {2}^{2} - 64 + {3}^{2} - ... - 64 + {10}^{2} = 2 - 64 \times 10 + \dfrac{10(10 + 1)(2 \times 10 + 1)}{6} = 2 - 640 + 385 = - 253 < 0$

$b = ( {1}^{1} - 64) \times ( {2}^{1} - 64) \times ( {3}^{1} - 64) \times ... \times ( {10}^{1} - 64) = (1 - 64) \times (2 - 64) \times (3 - 64) \times ... \times (10 - 64) = (- 63) \times (- 62) \times (- 61) \times ... \times (- 54) = 63 \times 62 \times 61 \times ... \times 54 > 0$

$\implies a < b$