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

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

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

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

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

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

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

XONG RỒI NHÉ BẠN TICK CHO MÌNH NHÉ

1-2+3-4+5-6+...+2021-2022+2023

=(1-2)+(3-4)+(5-6)+...+(2021-2022)+2023

=-1+-1+-1+-1+...+-1+2023(có 1011 số -1)

=-1011+2023
=1012

bài b làm tương tự

\(-7\left(x+9\right)-3\left(5-x\right)=2\\ \Rightarrow-7x-63-15+3x-2=0\\ \Rightarrow-4x-80=0\\ \Rightarrow-4x=80\\ \Rightarrow x=-20\)

-7x+(-63)-15+3x=2

[(-7x)+3x]+[(-63)-15]=2

-4x+(-78)=2

-4x=2+(-78)

-4x=-76

x=(-76)\(\div\)(-4)

x=19

\(-7x-63-15+3x=2\Leftrightarrow-4x-78=2\Leftrightarrow x=-20\)

-7(x+9)-3(5 -x) = 2

x=-20

\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{380}\)

\(=\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{19\cdot20}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{19}-\frac{1}{20}\)

\(=\frac{1}{2}-\frac{1}{20}=\frac{9}{20}\)

TL

\(\frac{1}{6}\)+\(\frac{1}{12}\)+\(\frac{1}{20}\)+....+\(\frac{1}{380}\)

=>\(\frac{1}{2.3}\)+\(\frac{1}{3.4}\)+\(\frac{1}{4.5}\)+...+\(\frac{1}{19.20}\)

=>\(\frac{1}{2}\)-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{4}\)+\(\frac{1}{4}\)+....+\(\frac{1}{19}\)-\(\frac{1}{20}\)

=>\(\frac{1}{2}\)-\(\frac{1}{20}\)

=>\(\frac{9}{20}\)

HT