1/72+1/90+1/110+1/132+1/156

Question

Виктория Соколова

Математика

18 декабря, 02:20

1/72+1/90+1/110+1/132+1/156

+3

Ответы (1)

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Алапа · Answer 1

1) 1/72 + 1/90 = 1 / (9 * 8) + 1 / (9 * 10) = 1 / (9 * 2 * 4) + 1 / (9 * 2 * 5) =

= (1 * 5) / (9 * 2 * 4 * 5) + (1 * 4) / (9 * 2 * 5 * 4) = (5 + 4) / (9 * 2 * 4 * 5) =

= 9 / (9 * 2 * 4 * 5) = 1 / (2 * 4 * 5);

2) 1 / (2 * 4 * 5) + 1/110 = 1 / (10 * 4) + 1 / (10 * 11) = 11 / (10 * 4 * 11) + 4 / (10 * 11 * 4) =

= (11 + 4) / (10 * 4 * 11) = (5 * 3) / (5 * 2 * 4 * 11) = 3 / (2 * 4 * 11);

3) 3 / (2 * 4 * 11) + 1/132 = 3 / (2 * 4 * 11) + 1 / (11 * 3 * 4) =

= (3 * 3) / (2 * 4 * 11 * 3) + 2 / (11 * 3 * 4 * 2) = 11 / (11 * 3 * 4 * 2) = 1/24;

4) 1/24 + 1/156 = 1 / (2 * 12) + 1 / (12 * 13) = (13 + 2) / (2 * 12 * 13) = (3 * 5) / (2 * 12 * 13) =

= 5/104.