\(3^{2x+2}=9^{x+3}\)

\(3^{2x+2}=\left(3^2\right)^{x+3}\)

\(3^{2x+2}=3^{2x+6}\)

\(\Rightarrow2x+2=2x+6\)(Vô Lý)

\(\Rightarrow\)Không có giá trị nào của x

 ko co gia tri nao cua x

\(2A=2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2011}}\)

=> \(2A-A=\left(2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2011}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2012}}\right)\)

=>  \(A=2-\frac{1}{2^{2012}}=\frac{2^{2013}-1}{2^{2012}}\)

\(A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2012}}\)

\(2A=2\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2012}}\right)\)

\(2A=3+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2011}}\)

\(2A-A=A\)

\(=\left(3+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2011}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2012}}\right)\)

\(=3+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2011}}-1-\frac{1}{2}-\frac{1}{2^2}-\frac{1}{2^3}-...-\frac{1}{2^{2012}}\)

\(=2-\frac{1}{2012^2}\)

 \(B=\left(\frac{1}{99}+\frac{12}{999}+\frac{123}{9999}\right)\cdot\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\)

\(B=\left(\frac{1}{99}+\frac{12}{999}+\frac{123}{9999}\right)\cdot\left(\frac{6}{12}-\frac{4}{12}-\frac{2}{12}\right)\)

\(B=\left(\frac{1}{99}+\frac{12}{999}+\frac{123}{9999}\right)\cdot0=0\)

(x + 1) + (x + 3) + (x + 5) + ... + (x + 15) = 128

=> x + 1 + x + 3 + x + 5 + ... + x + 15 = 128(bỏ dấu ngoặc)

=> (x + x + ... + x) + (1 + 3 + 5 + ... + 15) = 128 ( chia thành 2 nhóm)

+) Số số hạng là : (15 - 1) : 2 + 1 = 8

Tổng : (1 + 15).8 : 2 = 64

=> 8x + 64 = 128

=> 8x = 64

=> x = 8

Vậy x = 8

(x + 1) + (x + 4) + (x + 7) + ... + (x + 22) = 829

=> x + 1 + x + 4 + x + 7 + ... + x + 22= 829

=> (x + x + ... + x) + (1 + 4 + 7 + ... + 22) = 829

+) Số số hạng là : (22 - 1) : 3 + 1 = 8

Tổng : (1 + 22).8 : 2 = 92

=> 8x + 92 = 829

=> 8x = 737

=> x = 737/8 

a) (x + 1) + (x + 3) + (x + 5) + .... + (x + 15) = 128 (8 cặp số)

=> (x + x + ... + x) + (1 + 3 + 5 + ... + 15) = 128

       8 hạng tử x          8 số hạng

=> 8x + 8.(15 + 1) : 2 = 128

=> 8x + 64 = 128

=> 8x = 64

=> x = 8

b) (x + 1) + (x + 4) + (x + 7) +... + (x + 22) = 829 (8 cặp số)

=> (x + x + ... + x) + (1 + 4 + 7 +... + 22) = 829

    8 hạng tử x                    8 số hạng

=> 8x + 8.(22 + 1):2 = 829

=> 8x + 92 = 829

=> 8x = 737

=> x = 91,125

\(\frac{6^3+3\times6^2+3^3}{-13}=\frac{2^3\times3^3+3\times2^2\times3^2+3^3}{-13}\)

                                    \(=\frac{3^3\left(2^3+2^2+1\right)}{-13}\)

                                     \(=\frac{3^3\times13}{-13}\)

                                      \(=-27\)

Cảm Ơn !

\(1+\frac{1}{1+2}+\frac{1}{1+2+3}+...+\frac{1}{1+2+3+...+x}=2\)

\(\Rightarrow1+\frac{1}{2.3}.2+\frac{1}{3.4}.2+...+\frac{1}{x\left(x+1\right)}.2=2\)

=> \(2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}\right)=2\)

=> \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x\left(x+1\right)}=1\)

=> \(1-\frac{1}{x+1}=1\)

=> \(\frac{1}{x+1}=0\Rightarrow0\left(x+1\right)=1\Rightarrow x\in\varnothing\)

\(\frac{1}{1.2:2}+\frac{1}{2.3:2}+\frac{1}{3.4:2}+...+\frac{1}{x.\left(x+1\right):2}=2\)

\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{x.\left(x+1\right)}=2\)

\(2.\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\right)=2\)

\(1-\frac{1}{x+1}=1\)

\(\frac{1}{x+1}=0\)

Vậy x vô nghiệm.

\(\frac{30303}{80808}=\frac{3\times10101}{8\times10101}=\frac{3}{8}\)

\(3^{x+4}+3^{x+2}=270\)

\(< =>3^x.81+3^x.9=270\)

\(< =>3^x=\frac{270}{90}=3< =>x=1\)

\(3^{x+4}+3^{x+2}=270\)

\(\Leftrightarrow3^x.81+3^x.9=270\)

\(\Leftrightarrow3^x\left(81+9\right)=270\)

\(\Leftrightarrow3^x.90=270\)

\(\Leftrightarrow3^x=3\)

\(\Leftrightarrow x=1\)

Đặt A=2.2².2³.2⁴...2¹⁰⁰

2A=2(2.2².2³.2⁴...2¹⁰⁰)

2A=2².2³.2⁴...2¹⁰¹

2A-A=2¹⁰¹-2

A=2¹⁰¹-2/2

Động Từ :

Put , do , pick , go , get , have , study , sing , catch , dance

Danh từ :

dog , cat , hat , shirt , balloon , print , piano , bass , computer , maracas

10 động từ là:go,jum,sing,dance,sleep,water,wash,write,read,cry

9 danh từ là:flower,sand,family,home,house,book,pen,computer,clock

ks nhé!Học tốt!