Sửa đề: \(A=1-\dfrac{3}{4}+\left(\dfrac{3}{4}\right)^2-\left(\dfrac{3}{4}\right)^3+...-\left(\dfrac{3}{4}\right)^{2019}\)

\(\Leftrightarrow A\cdot\dfrac{3}{4}=\dfrac{3}{4}-\left(\dfrac{3}{4}\right)^2+...-\left(\dfrac{3}{4}\right)^{2020}\)

=>\(A\cdot\left(\dfrac{3}{4}+1\right)=\dfrac{3}{4}-\left(\dfrac{3}{4}\right)^2+...-\left(\dfrac{3}{4}\right)^{2020}+1-\dfrac{3}{4}+...-\left(\dfrac{3}{4}\right)^{2019}\)

=>\(A\cdot\dfrac{7}{4}=\dfrac{-3^{2020}}{4^{2020}}+1=\dfrac{4^{2020}-3^{2020}}{4^{2020}}\)

=>\(A=\dfrac{4^{2020}-3^{2020}}{4^{2019}\cdot7}\) không phải là số nguyên

48 nha

--5²²-{-222-[-122-(100-5²²)+2024]}

--5²²-{-222-[-122-95²²+2024]}

--5²²-{-222+ 122-95²²+2024}

--5²²+ 2029²²

2034²²

=-5^22+222-112-100+5^22+2022

=(-5^22+5^22)+(222-112-100)+2022

=0+0+2022

=2022

\(\dfrac{4}{3}+\dfrac{-11}{31}+\dfrac{3}{10}-\dfrac{20}{31}-\dfrac{2}{5}\)

\(=\dfrac{4}{3}+\left(\dfrac{3}{10}-\dfrac{2}{5}\right)+\left(-\dfrac{11}{31}-\dfrac{20}{31}\right)\)

\(=\dfrac{4}{3}-1-\dfrac{1}{10}=\dfrac{1}{3}-\dfrac{1}{10}=\dfrac{7}{30}\)

bài 2:

a: \(A=\dfrac{1}{5}+\dfrac{1}{5^2}+...+\dfrac{1}{5^{2014}}\)

=>\(5A=1+\dfrac{1}{5}+...+\dfrac{1}{5^{2013}}\)

=>\(5A-A=1+\dfrac{1}{5}+...+\dfrac{1}{5^{2013}}-\dfrac{1}{5}-\dfrac{1}{5^2}-...-\dfrac{1}{5^{2024}}\)

=>\(4A=1-\dfrac{1}{5^{2024}}\)

=>\(A=\dfrac{1}{4}-\dfrac{1}{4\cdot5^{2024}}< \dfrac{1}{4}\)

ở cuối là -12¹⁰nha

help

Chiều rộng HCN là:

\(\dfrac{21}{10}:\dfrac{7}{2}=\dfrac{21}{10}x\dfrac{2}{7}=\dfrac{3}{5}x\dfrac{1}{1}=\dfrac{3}{5}\)

789000 chiều dài hcn là m mà bạn?

Sửa đề: Diện tích là \(\dfrac{21}{10}m^2\)

Chiều rộng hình chữ nhật là:

\(\dfrac{21}{10}:\dfrac{7}{2}=\dfrac{21}{10}\times\dfrac{2}{7}=\dfrac{42}{70}=0,6\left(m\right)\)