Question

ПОМОГИТЕ ПЛЗ! РАЦИОНАЛЬНЫЙ СПОСОБ! 6 КЛАСС!
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Answer 1

1 и 2

решаются одинаково

1/n*(n+1) = (n + 1 - n)/n(n + 1) = 1/n - 1/(n + 1)

1. 1/1*2 + 1/2*3 + 1/3*4 + ..... + 1/9*10 = (1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + ... + (1/9 - 1/10) = 1 - 1/10 = 9/10

2. 1/10*11 + 1/11*12 + .... + 1/19*20 = (1/10 - 1/11) + (1/11 - 1/12) + .... + (1/19 - 1/20) = 1/10 - 1/20 = 1/20

3. 3*7*11*13*37 =   111111

5/111111 + 5/222222 - 4/111111 = 1/111111 + 5/222222 = 7/222222

10101 * 7/222222 = 7/22