Вычислить: 1-1/72-1/90-1/110-1/132-1/156-1/182-1/210

Вычислим пример по деяниям:

1) 1 - 1/72 = 72/72 - 1/72 = (72 - 1)/72 = 71/72;

2) 71/72 - 1/90 = 71/(4 * 2 * 9) - 1/(9 * 2 * 5) = 71 * 5/(4 * 2 * 9 * 5) - 4/(9 * 2 * 5 * 4) = (355 - 4)/360 = 351/360;

3) 351/360 - 1/110 = 351/(36 * 10) - 1/(11 * 10) = 351 * 11/(36 * 10 * 11) - 36/(11 * 10 * 36) = (3861 - 36)/3960 = 3825/3960 = 255/264;

4) 255/264 - 1/132 = 255/264 - 2/264 = (255 - 2)/264 = 253/264 = 23/24 ;

5) 23/24 - 1/156 = 13 * 23/312 - 2/312 = (299 - 2)/312 = 297/312 = 99/104;

6) 99/104 - 1/182 = 693/728 - 4/728 = 689/728 = 53/56;

7) 53/56 - 1/210 = 795/840 - 4/840 = 791/840 = 113/120.

Ответ: 113/120.