Question

Rút gon số hữu tỉ:

\(C=\frac{1}{2}+\left(\frac{1}{2}\right)^2+......+\left(\frac{1}{2}\right)^{99}\)

Làm ơn giúp nha 

Answer 1

\(\frac{1}{2}.C=\left(\frac{1}{2}\right)^2+\left(\frac{1}{2}\right)^3+...+\left(\frac{1}{2}\right)^{100}\)

\(C-\frac{1}{2}.C=\left[\frac{1}{2}+\left(\frac{1}{2}\right)^2+...+\left(\frac{1}{2}\right)^{99}\right]-\left[\left(\frac{1}{2}\right)^2+\left(\frac{1}{2}\right)^3+...+\left(\frac{1}{2}\right)^{100}\right]\)

\(\frac{1}{2}.C=\frac{1}{2}-\left(\frac{1}{2}\right)^{100}=\frac{1}{2}-\frac{1}{2^{100}}\)

\(C=\left(\frac{1}{2}-\frac{1}{2^{100}}\right):\frac{1}{2}\)

\(C=\left(\frac{1}{2}-\frac{1}{2^{100}}\right).2=1-\frac{1}{2^{99}}\)