a) chung minh 5+5^2+5^3+…+5^2020=3^2020-5/4

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Môn Toán Farah 4 years 2020-11-24T15:41:45+00:00 2020-11-24T15:41:45+00:00 1 Answers 50 views 0

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Captcha* Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )

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Eirian · Answer 1 · 2020-11-24T15:43:29+00:00

Eirian

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2020-11-24T15:43:29+00:00 November 24, 2020 at 3:43 pm

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Bạn tham khảo :

Đặt $A = 5 + 5^{2} + 5^{3} + \dots + 5^{2020}$

⇒ $5^{2} A = 5^{2} + 5^{3} + 5^{4} + \dots + 5^{2020}$

⇒ $5^{2} A - A = (5^{2} + 5^{3} + 5^{4} + \dots + 5^{2022}) - (5 + 5^{2} + 5^{3} + \dots + 5^{2020})$

⇒ $24 A = 5^{2022} - 5$

⇒ $A = \frac{5^{2022}}{-} 524$

⇒ $A = \frac{5^{2022} . 24 - 5}{24}$

⇒ $A = \frac{5^{2} 022. 23}{24}$

Ta có :

$3^{2020} - \frac{5}{4} = \frac{3^{2020} .4}{4} - \frac{5}{4} = \frac{3^{2020} - 5}{4} = \frac{3^{2020} - 5.6}{24} = \frac{3^{2020} - 30}{24}$

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