\(A=2^{100}-2^{99}+2^{98}-2^{97}+....+2^2-2\)

\(2A=2^{101}-2^{100}+2^{99}-2^{98}+....+2^3-2^2\)

\(2A+A=2^{101}-2\)

\(A=\frac{2^{101}-2}{3}\)

b) tương tự

\(B=\frac{3^{101}+1}{4}\)

\(A=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\)

\(2A=2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2\)

\(2A+A=2^{101}-2\)

\(A=\frac{2^{101}-2}{3}\)

\(B=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{99}}\)

\(3B=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{98}}\)

\(3B-B=1-\frac{1}{3^{99}}\)

\(B=\frac{1-\frac{1}{3^{99}}}{2}\)

\(A=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\)

\(2A=2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2\)

\(2A+A=\left(2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-^2\right)+\left(2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\right)\)

\(3A=2^{101}-2\)

\(A=\frac{2^{101}-2}{3}\)

Chúc bạn học tốt ~ 

Ta có: 2^300=(2^3)^100=8^100

           3^200=(3^2)^100=9^100

Do 8<9 => 8^100<9^100

Hay 2^300<3^200

k cho mik nhé !

Bài 1: so sánh  2³⁰⁰ và 3²⁰⁰

Bài làm

Ta có 2³⁰⁰=(2³)¹⁰⁰=8¹⁰⁰

          2²⁰⁰=(2²)¹⁰⁰=4¹⁰⁰

Vì 8¹⁰⁰>4¹⁰⁰

Nên 2³⁰⁰>2²⁰⁰

Vậy 2³⁰⁰>2²⁰⁰

C =\(\frac{1}{100}-\frac{1}{100.99}-...\)\(-\frac{1}{3.2}-\frac{1}{2.1}\)

C = \(\frac{1}{100}-\frac{1}{100}+\frac{1}{99}-\frac{1}{99}+...\)\(+\frac{1}{3}-\frac{1}{3}+\frac{1}{2}-\frac{1}{2}+1\)

C = 1

Ta có:

\(2.3^x+3^{x+2}=99\)

\(=2.3^x+3^x.3^2=99\)

\(\Rightarrow3^x\left(2+3^2\right)=99\)

\(\Rightarrow3^x.11=99\)
\(\Rightarrow3^x=99:11=9\)

\(\Rightarrow x=2\)

Vậy x = 2

a/ \(\left|x-3\right|=x+1\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=x+1\\x-3=-x-1\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x-x=1+3\\x+x=-1+3\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}0x=4\left(loại\right)\\2x=2\end{matrix}\right.\) \(\Leftrightarrow x=1\)

Vậy ...

b/ \(\left|x-2\right|=2x+3\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=2x+3\\x-2=-2x-3\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}2x-x=-2-3\\x+2x=-3+2\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=-5\\x=-\dfrac{1}{3}\end{matrix}\right.\)

Vậy ,..

đáp án:6993/13

minh tinh ra x = -3

viết thế này bố thằng nào hiểu được

mk nè bn k trước đi

mk nua