Question

M = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 +1/64 + 1/128 + 1/256 + 1/512 . 

Answer 1

\(M=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{512}\)

\(2M=1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{256}\)

\(2M-M=\left(1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{256}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{512}\right)\)

\(M=1-\frac{1}{512}=\frac{511}{512}\)