Question

Tính tổng cơ số A=1+1/2+(1/2)^2+(1/2)^3+...+(1/2)^100

giúp mik vs ạ mk đg cần gấp ạ

Answer 1

Ta có \(A=1+\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{100}}\Rightarrow2A=2+1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{99}}\Rightarrow2A-A=2+\left(1-1\right)+\left(\dfrac{1}{2}-\dfrac{1}{2}\right)+\left(\dfrac{1}{2^2}-\dfrac{1}{2^2}\right)+...+\left(\dfrac{1}{2^{99}}-\dfrac{1}{2^{99}}\right)-\dfrac{1}{2^{100}}\Rightarrow A=2-\dfrac{1}{2^{100}}=\dfrac{2^{101}-1}{2^{100}}\)Vậy \(A=\dfrac{2^{101}-1}{2^{100}}\)