Toán Lớp 7: Cho A=1-3/4+(3/4)^2-(3/4)^3+(3/4)^4-…-(3/4)^2019+(3/4)^2020
a) Tính A
b) Chứng minh A không phải số nguyên
Leave a reply
Register Now
Login
Lost Password
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Toán Lớp 7: Cho A=1-3/4+(3/4)^2-(3/4)^3+(3/4)^4-…-(3/4)^2019+(3/4)^2020
a) Tính A
b) Chứng minh A không phải số nguyên
Comments ( 2 )
#helichange
A = 1 – \dfrac34 + \left(\dfrac34\right)^2 – \left(\dfrac34\right)^3 + \left(\dfrac34\right)^4 – \cdots – \left(\dfrac34\right)^{2019} + \left(\dfrac34\right)^{2020}\\
\Leftrightarrow \dfrac34A = \dfrac34 – \left(\dfrac34\right)^2+ \left(\dfrac34\right)^3 – \left(\dfrac34\right)^4 +\cdots-\left(\dfrac34\right)^{2020} + \left(\dfrac34\right)^{2021}\\
\Leftrightarrow A + \dfrac34A = 1 + \left(\dfrac34\right)^{2021}\\
\Leftrightarrow \dfrac74A = 1 + \left(\dfrac34\right)^{2021}\\
\Leftrightarrow A = \dfrac47 + \dfrac47\cdot \left(\dfrac34\right)^{2021}\\
\text{Giả sử}\ A \in\Bbb Z\\
\Leftrightarrow 7A \in\Bbb Z\\
\Leftrightarrow 4 + 4\cdot \left(\dfrac34\right)^{2021}\in\Bbb Z\\
\Leftrightarrow \left(\dfrac34\right)^{2021}\in\Bbb Z\quad \text{(vô lí)}\\
\Rightarrow \text{Điều giả sử sai}\\
\Rightarrow A\notin\Bbb Z
\end{array}\)