a,Tính tổng:S=1+52+54+...+5200

=>5²S=5²+5⁴+5⁶+...+5²⁰²

=>25S-S=24S=5²⁰²-1

=>S=\(\frac{5^{202}-1}{24}\)

b,So sánh 230+330+430 và 3.2410

3.24^10=3^11.4^15 
4^30=4^15.4^15 
hiển nhiên 4^15>3^11 
=>3.24^10<<4^30<<<2^30+3^20+4^30

Ta có: 2³⁰+3³⁰+4³⁰>2³⁰+2³⁰+4³⁰=2³¹+2³⁰.2³⁰

                                                                 =2³¹(1+2²⁹) (1)

Lại có:3.24^10=3^11.2^30 (2)

So sánh (1)và (2): Vì 3^11<4^11=2^22<2^29

                              và 2^30<2^31

=> 3^11.2^30 <(1+2^29)2^31<2^30+3^30+4^30

Ta có A = 5 + 5² + 5³ + ... + 5²⁰²¹

5A = 5² + 5³ + 5⁴ + ... + 5²⁰²²

5A - A = ( 5² + 5³ + 5⁴ + ... + 5²⁰²² ) - ( 5 + 5² + 5³ + ... + 5²⁰²¹ )

4A = 5²⁰²² - 5

A = \(\dfrac{5^{2022}-5}{4}\)

Tìm chữ số tận cùng của kết quả mỗi phép tính sau:

a. 49¹⁵

b. 54¹⁰

c. 11²⁰+119²¹+2000²²

Ta có:

( 5 2 - 1).P = ( 5 2  – 1).12.( 5 2  + 1)( 5 4  + 1)( 5 8  + 1)( 5 16  + 1)

= 12.(  5 2  – 1).( 5 2  + 1)( 5 4 + 1)( 5 8  + 1)( 5 16 + 1)

= 12.(  5 4  - 1)(  5 4  + 1)(  5 8  + 1)( 5 16  + 1)

= 12.(  5 8  - 1)(  5 8  + 1)( 5 16  + 1)

= 12.(  5 16  - 1)( 5 16  + 1)

= 12.(  5 32  - 1)

-7/13,-2/3

-7/13 ;  3/5

\(\dfrac{-7}{13};\dfrac{-2}{3}\)

\(1,\\ \left(x-7\right)^{x+1}-\left(x-7\right)^{x+11}=0\\ \Leftrightarrow\left(x-7\right)^{x+1}\left[1-\left(x-7\right)^{10}\right]=0\\ \Leftrightarrow\left[{}\begin{matrix}\left(x-7\right)^{x+1}=0\\\left(x-7\right)^{10}=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-7=0\\x-7=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=7\\x=8\end{matrix}\right.\)

\(2,\\ a,\left|2x-3\right|>5\Leftrightarrow\left[{}\begin{matrix}2x-3< -5\\2x-3>5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x< -1\\x>4\end{matrix}\right.\\ b,\left|3x-1\right|\le7\Leftrightarrow\left[{}\begin{matrix}3x-1\le7\\1-3x\le7\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x\le\dfrac{8}{3}\\x\ge-2\end{matrix}\right.\\ c,\cdot x< -\dfrac{3}{2}\\ \Leftrightarrow5-3x+\left(-2x-3\right)=7\Leftrightarrow2-5x=7\Leftrightarrow x=-1\left(ktm\right)\\ \cdot-\dfrac{3}{2}\le x\le\dfrac{5}{3}\\ \Leftrightarrow\left(5-3x\right)+\left(2x+3\right)=7\Leftrightarrow8-x=7\Leftrightarrow x=1\left(tm\right)\\ \cdot x>\dfrac{5}{3}\\ \Leftrightarrow\left(3x-5\right)+\left(2x+3\right)=7\Leftrightarrow5x-2=7\Leftrightarrow x=\dfrac{9}{5}\left(tm\right)\\ \Leftrightarrow S=\left\{1;\dfrac{9}{5}\right\}\)

Mai lam

\(\dfrac{14}{21}=\dfrac{7\cdot2}{7\cdot3}=\dfrac{2}{3}\)

\(\dfrac{-36}{48}=\dfrac{-12\cdot3}{12\cdot4}=-\dfrac{3}{4}\)

\(\dfrac{28}{-52}=\dfrac{7\cdot4}{-4\cdot13}=-\dfrac{7}{13}\)

\(\dfrac{-54}{-90}=\dfrac{-18\cdot3}{-18\cdot5}=\dfrac{3}{5}\)

\(\dfrac{14}{21}\) =\(\dfrac{2}{3}\)

\(\dfrac{-36}{48}\) =\(\dfrac{3}{4}\)

\(\dfrac{28}{-52}\)=\(\dfrac{7}{-13}\)

\(\dfrac{-54}{-90}\) =\(\dfrac{6}{9}=\dfrac{2}{3}\)

\(\dfrac{14}{21}=\dfrac{2}{3}\)

\(\dfrac{-36}{48}=-\dfrac{3}{4}\)

\(\dfrac{28}{-52}=-\dfrac{7}{13}\)

\(\dfrac{-54}{-90}=\dfrac{3}{5}\)

a, 18/54 = 1/3 

b, 1/3 = 1/5 +2/15

a) \(\frac{18}{54}=\frac{1}{3}\)

b) \(\frac{18}{54}=\frac{1}{5}+\frac{2}{15}\)

~Học tốt~

\(a,\dfrac{52}{32}=\dfrac{13}{8}\\ \dfrac{55}{65}=\dfrac{11}{13}\\ MSC:104\\ =>\dfrac{13}{8}=\dfrac{13.13}{8.13}=\dfrac{169}{104}\\ \dfrac{11}{13}=\dfrac{11.8}{13.8}=\dfrac{88}{104}\)

\(b,\dfrac{72}{64}=\dfrac{9}{8}\\ \dfrac{54}{81}=\dfrac{2}{3}\\ MSC:24\\ \dfrac{9}{8}=\dfrac{9.3}{8.3}=\dfrac{27}{24}\\ \dfrac{2}{3}=\dfrac{2.8}{3.8}=\dfrac{16}{24}\\ c,\dfrac{24}{36}=\dfrac{2}{3}\\ \dfrac{12}{30}=\dfrac{2}{5}\\ MSC:15\\ \dfrac{2}{3}=\dfrac{2.5}{3.5}=\dfrac{10}{15}\\ \dfrac{2}{5}=\dfrac{2.3}{3.5}=\dfrac{6}{15}\)

\(d,\dfrac{80}{40}=2\\ \dfrac{45}{63}=\dfrac{5}{7}\\ MSC:7\\ 2=\dfrac{14}{7}\\ e,\dfrac{150}{50}=3\\ \dfrac{100}{200}=\dfrac{1}{2}\\ MSC:2\\ 3=\dfrac{6}{2}\\ f,\dfrac{54}{81}=\dfrac{2}{3}\\ \dfrac{69}{93}=\dfrac{23}{21}\\ MSC:21\\ \dfrac{2}{3}=\dfrac{2.7}{3.7}=\dfrac{14}{21}\)

\(a.\dfrac{52}{32}\text{=}\dfrac{13}{8};\dfrac{55}{65}\text{=}\dfrac{11}{13}\)

\(\dfrac{13.13}{13.8}\text{=}\dfrac{169}{104};\dfrac{11.8}{13.8}\text{=}\dfrac{88}{104}\)

\(c.\dfrac{24}{36}\text{=}\dfrac{2}{3};\dfrac{12}{30}\text{=}\dfrac{2}{5}\)

\(\dfrac{2.5}{3.5}\text{=}\dfrac{10}{15};\dfrac{2.3}{5.3}\text{=}\dfrac{6}{15}\)

\(b.\dfrac{72}{64}\text{=}\dfrac{9.3}{8.3}\text{=}\dfrac{27}{24};\dfrac{54}{81}\text{=}\dfrac{2.8}{3.8}\text{=}\dfrac{16}{24}\)

\(d.\dfrac{80}{40}\text{=}\dfrac{2.63}{63}\text{=}\dfrac{126}{63};\dfrac{45}{63}\)

\(e.\dfrac{150}{50}\text{=}\dfrac{3.2}{2}\text{=}\dfrac{6}{2};\dfrac{100}{200}\text{=}\dfrac{1}{2}\)

\(f.\dfrac{54}{81}\text{=}\dfrac{2.31}{3.31}\text{=}\dfrac{62}{93};\dfrac{69}{93}\)

a) \(7^3.7^5=7^{3+5}=7^8\)

b)\(5^6.5^4=5^{6+4}=5^{10}\)

14/21=2/3; -36/48=-2/3

28/-52=-7/13; -54/-90=3/5

-21/39=-7/13

-21/39=-7/13=-14/26=-21/39=-28/52=-35/65=-42/78=-48/91

`14/21=2/3`

`(-36)/48=-3/4`

`28/(-52)=-7/13`

`(-54)/(-90)=3/5`

`(-21)/39=-7/13`