\(C=5+\dfrac{5}{2}+\dfrac{5}{2^2}+...+\dfrac{5}{2^{10}}\)
\(2C=2\left(5+\dfrac{5}{2}+\dfrac{5}{2^2}+...+\dfrac{5}{2^{10}}\right)\)
\(2C=10+5+\dfrac{5}{2}+...+\dfrac{5}{2^9}\)
\(2C-C=\left(10+5+\dfrac{5}{2}+...+\dfrac{5}{2^9}\right)-\left(5+\dfrac{5}{2}+...+\dfrac{5}{2^{10}}\right)\)
\(C=10-\dfrac{5}{2^{10}}\)