Question

S = 1/2 + 1/2^2 + … + 1/2^2005 Plzzzz 🙏🙏🙏🙏

Answer 1

\(S=\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{2005}}\)

\(\Rightarrow2S=1+\dfrac{1}{2}+...+\dfrac{1}{2^{2004}}\)

\(\Rightarrow2S-S=\left(1+\dfrac{1}{2}+...+\dfrac{1}{2^{2004}}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{2005}}\right)\)

\(\Rightarrow S=1-\dfrac{1}{2^{2005}}\).