Toán a) chung minh 5+5^2+5^3+…+5^2020=3^2020-5/4 18/07/2021 By Samantha a) chung minh 5+5^2+5^3+…+5^2020=3^2020-5/4
Bạn tham khảo : Đặt $A = 5 + 5^2 + 5^3 +… + 5^{2020}$ ⇒ $5^2A = 5^2 + 5^3 + 5^4 + … + 5^{2020}$ ⇒ $5^2A -A = ( 5^2 + 5^3 + 5^4 + … + 5^{2022}) – ( 5+ 5^2 + 5^3+ … + 5^{2020})$ ⇒ $24A = 5^{2022} – 5$ ⇒ $A = \dfrac{5^{2022}} – {5}{24}$ ⇒ $A = \dfrac{5^{2022} . 24 – 5}{24}$ ⇒ $A = \dfrac{5^2022. 23}{24}$ Ta có : $3^{2020} – \dfrac{5}{4} = \dfrac{3^{2020}.4}{4} – \dfrac{5}{4} = \dfrac{3^{2020} – 5}{4}=\dfrac{3^{2020} – 5 . 6}{24}= \dfrac{3^{2020} – 30}{24}$ Đến đây tịt rồi @@ Trả lời
Bạn tham khảo :
Đặt $A = 5 + 5^2 + 5^3 +… + 5^{2020}$
⇒ $5^2A = 5^2 + 5^3 + 5^4 + … + 5^{2020}$
⇒ $5^2A -A = ( 5^2 + 5^3 + 5^4 + … + 5^{2022}) – ( 5+ 5^2 + 5^3+ … + 5^{2020})$
⇒ $24A = 5^{2022} – 5$
⇒ $A = \dfrac{5^{2022}} – {5}{24}$
⇒ $A = \dfrac{5^{2022} . 24 – 5}{24}$
⇒ $A = \dfrac{5^2022. 23}{24}$
Ta có :
$3^{2020} – \dfrac{5}{4} = \dfrac{3^{2020}.4}{4} – \dfrac{5}{4} = \dfrac{3^{2020} – 5}{4}=\dfrac{3^{2020} – 5 . 6}{24}= \dfrac{3^{2020} – 30}{24}$
Đến đây tịt rồi @@