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nastya16029
@nastya16029
April 2021
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ПОМОГИТЕ ПЖ!!!ОЧЕНЬ СРОЧНО!!!!!!!
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nelle987
Verified answer
1) 1 + 7 + 13 + ... + (6n - 5) = 280 (n - натуральное)
Сумма прогрессии в левой части равна
(1 + 6n-5) * n / 2 = 280
(6n - 4) * n / 2 = 280
(3n - 2) * n = 280
3n^2 - 2n - 280 = 0
D/4 = 1 + 3*280 = 841 = 29^2
n = (1 + 29)/3 = 10 (второй корень нецелый)
x = 6n - 5 = 55
2) (x - 1)/x + (x - 2)/x + ... + 1/x = 3
1 + 2 + ... + (x - 1) = 3x
x * (x - 1) / 2 = 3x | : x ≠ 0
x - 1 = 6
x = 7
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Answers & Comments
Verified answer
1) 1 + 7 + 13 + ... + (6n - 5) = 280 (n - натуральное)Сумма прогрессии в левой части равна
(1 + 6n-5) * n / 2 = 280
(6n - 4) * n / 2 = 280
(3n - 2) * n = 280
3n^2 - 2n - 280 = 0
D/4 = 1 + 3*280 = 841 = 29^2
n = (1 + 29)/3 = 10 (второй корень нецелый)
x = 6n - 5 = 55
2) (x - 1)/x + (x - 2)/x + ... + 1/x = 3
1 + 2 + ... + (x - 1) = 3x
x * (x - 1) / 2 = 3x | : x ≠ 0
x - 1 = 6
x = 7