Question

C=1+1\2+(1\2)^2+(1\2)^3+...+(1\2)^100

giúp mình với nha

Answer 1

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