Question

help em phần này gấp vs (huhu ko bt công thức)

Answer 1

s: \(\dfrac{-21}{46}\cdot\left(-13\right)+\dfrac{3^2}{-9}-\dfrac{-1}{2}\cdot\left(-10\right)\)

\(=\dfrac{21}{46}\cdot13-1-\dfrac{1}{2}\cdot10\)

\(=\dfrac{273}{46}-1-5=\dfrac{273}{46}-5=\dfrac{43}{46}\)

t: \(T=\left(-\dfrac{1}{7}\right)+\left(-\dfrac{1}{7}\right)^2+...+\left(-\dfrac{1}{7}\right)^{2024}\)

=>\(\left(-\dfrac{1}{7}\right)\cdot T=\left(-\dfrac{1}{7}\right)^2+\left(-\dfrac{1}{7}\right)^3+...+\left(-\dfrac{1}{7}\right)^{2025}\)

=>\(\left(-\dfrac{1}{7}\right)\cdot T-T=\left(-\dfrac{1}{7}\right)^2+\left(-\dfrac{1}{7}\right)^3+...+\left(-\dfrac{1}{7}\right)^{2025}-\left(-\dfrac{1}{7}\right)-\left(-\dfrac{1}{7}\right)^2-...-\left(-\dfrac{1}{7}\right)^{2024}\)

=>\(-\dfrac{8}{7}T=\left(-\dfrac{1}{7}\right)^{2025}+\dfrac{1}{7}\)

=>\(-\dfrac{8}{7}\cdot T=-\dfrac{1}{7^{2025}}+\dfrac{1}{7}\)

=>\(-\dfrac{8}{7}\cdot T=\dfrac{-1+7^{2024}}{7^{2025}}\)

=>\(T\cdot\dfrac{8}{7}=\dfrac{-7^{2024}+1}{7^{2025}}\)

=>\(T=\dfrac{-7^{2024}+1}{7^{2025}}:\dfrac{8}{7}=\dfrac{-7^{2024}+1}{7^{2024}}\cdot8\)

u: \(U=\dfrac{1}{5}-\dfrac{1}{5^2}+\dfrac{1}{5^3}-...-\dfrac{1}{5^{2024}}\)

=>\(5\cdot U=1-\dfrac{1}{5}+\dfrac{1}{5^2}-...-\dfrac{1}{5^{2023}}\)

=>\(5U+U=1-\dfrac{1}{5}+\dfrac{1}{5^2}-...-\dfrac{1}{5^{2023}}+\dfrac{1}{5}-\dfrac{1}{5^2}+...-\dfrac{1}{5^{2024}}\)

=>\(6U=1-\dfrac{1}{5^{2024}}=\dfrac{5^{2024}-1}{5^{2024}}\)

=>\(U=\dfrac{5^{2024}-1}{5^{2024}\cdot6}\)