Question

Tính:

S = \(\dfrac{1}{2}\) - \(\dfrac{1}{2^2}\) + \(\dfrac{1}{2^3}\) - \(\dfrac{1}{2^4}\) + ... + \(\dfrac{1}{2^{99}}\) - \(\dfrac{1}{2^{100}}\)

Answer 1

\(S=\dfrac{1}{2}-\dfrac{1}{2^2}+\dfrac{1}{2^3}-\dfrac{1}{2^4}+...+\dfrac{1}{2^{99}}-\dfrac{1}{2^{100}}\\ 2S=1-\dfrac{1}{2}+\dfrac{1}{2^2}-\dfrac{1}{2^3}+...+\dfrac{1}{2^{98}}-\dfrac{1}{2^{99}}\\ 2S+S=1-\dfrac{1}{2^{100}}\\ S=\dfrac{1-\dfrac{1}{2^{100}}}{3}\)