Question

B=-1/3+1/3^2-1/3^3+...+1/3^100-3/3^101

làm đúng và nhanh thì mình tick cho nha

 

Answer 1

\(3B=-1+\frac{1}{3}-\frac{1}{3^2}+...+\frac{1}{3^{99}}-\frac{1}{3^{100}}\)

\(3B+B=\left(-1+\frac{1}{3}-\frac{1}{3^2}+...+\frac{1}{3^{99}}-\frac{1}{3^{100}}\right)+\left(\frac{-1}{3}+\frac{1}{3^2}-\frac{1}{3^3}+...+\frac{1}{3^{100}}-\frac{1}{3^{101}}\right)\)

\(4B=-1-\frac{1}{3^{101}}\)

\(B=\frac{-\left(1+\frac{1}{3^{101}}\right)}{4}\)

Answer 2

\(3B=-1+\frac{1}{3}-\frac{1}{3^2}+...+\frac{1}{3^{99}}-\frac{1}{3^{100}}\)

\(3B+B=\left(-1+\frac{1}{3}-\frac{1}{3^2}+...+\frac{1}{3^{99}}-\frac{1}{3^{100}}\right)+\left(\frac{-1}{3}+\frac{1}{3^2}-\frac{1}{3^3}+...+\frac{1}{3^{100}}-\frac{1}{3^{101}}\right)\)

\(4B=-1-\frac{1}{3^{101}}\)

\(B=\frac{-\left(1+\frac{1}{3^{101}}\right)}{4}\)