Question

B

Answer 1

a) \(A=\dfrac{3}{4}:\left(\dfrac{2}{3}-\dfrac{5}{9}\right)+\dfrac{9}{4}\)

\(A=\dfrac{3}{4}:\left(\dfrac{6}{9}-\dfrac{5}{9}\right)+\dfrac{9}{4}\)

\(A=\dfrac{3}{4}:\dfrac{1}{9}+\dfrac{9}{4}\)

\(A=\dfrac{3}{4}\cdot9+\dfrac{9}{4}\)

\(A=\dfrac{27}{4}+\dfrac{9}{4}\)

\(A=\dfrac{36}{4}=9\) 

b) \(B=1+3^2+3^4+...+3^{98}-\dfrac{3^{100}}{8}\)

Đặt: \(C=1+3^2+3^4+...+3^{98}\)

\(9C=3^2+3^4+3^6+...+3^{100}\)

\(9C-C=\left(3^2+3^4+...+3^{100}\right)-\left(1+3^2+3^4+...+3^{98}\right)\)

\(8C=3^{100}-1\)

\(C=\dfrac{3^{100}-1}{8}\)

\(\Rightarrow B=\dfrac{3^{100}-1}{8}-\dfrac{3^{100}}{8}\)

\(B=\dfrac{3^{100}-1-3^{100}}{8}\)

\(B=\dfrac{-1}{8}\)