Question

C=2+2^2+2^3+.....+2^100-2^101

Answer 1

\(\Rightarrow2C=2^2+2^3+...+2^{101}-2^{102}\)

\(\Rightarrow C=2C-C=2^2+2^3+...+2^{101}-2^{102}-2-2^2-...-2^{100}+2^{101}\)

\(\Rightarrow C=2.2^{101}-2^{102}-2=2^{102}-2^{102}-2=-2\)

Answer 2

\(C=2+2^2\)+\(2^3\)+\(2^4\)+...+\(2^{101}\)

\(2C=\)\(2^2\)+\(2^3\)+\(2^4\)+...+\(2^{101}\)+\(2^{102}\)

\(2C-C\)=(\(2^2\)+\(2^3\)+\(2^4\)+...+\(2^{102}\))\(-\)(\(2\)+\(2^2\)+\(2^3\)+...+\(2^{101}\))

\(C\)=\(2^{102}\)\(-\)\(2\)

XONG RỒI NHÉ BẠN TICK CHO MÌNH NHÉ