Đặt A = \(\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+...+\frac{1}{100^2}\)

Ta có \(A=\frac{1}{3\cdot3}+\frac{1}{4\cdot4}+\frac{1}{5\cdot5}+...+\frac{1}{100\cdot100}\)

\(\Rightarrow A< \frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{99\cdot100}\)

\(\Rightarrow A< \frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)

\(\Rightarrow A< \frac{1}{2}-\frac{1}{100}< \frac{1}{2}\)

\(\Rightarrow A< \frac{1}{2}\left(đpcm\right)\)

\(\frac{1}{3^2}\)\(< \frac{1}{2.3}\)

\(\frac{1}{4^2}\)\(< \frac{1}{3.4}\)

\(...................\)

\(\frac{1}{100^2}\)\(< \frac{1}{99.100}\)

\(=>\)\(\frac{1}{3^2}\)\(+\frac{1}{4^2}\)\(+...+\frac{1}{100^2}\)\(< \frac{1}{2.3}\)\(+\frac{1}{3.4}\)\(+...+\frac{1}{99.100}\)

\(=>\)\(\frac{1}{3^2}\)\(+\frac{1}{4^2}\)\(+...+\frac{1}{100^2}\)\(< \frac{1}{2}\)\(-\frac{1}{3}\)\(+\frac{1}{3}\)\(-\frac{1}{4}\)\(+...+\frac{1}{99}\)\(-\frac{1}{100}\)

\(=>\)\(\frac{1}{3^2}\)\(+\frac{1}{4^2}\)\(+...+\frac{1}{100^2}\)\(< \frac{1}{2}\)\(-\frac{1}{100}\)\(< \frac{1}{2}\)

Vậy: \(\frac{1}{3^2}\)\(+\frac{1}{4^2}\)\(+...+\frac{1}{100^2}\)\(< \frac{1}{2}\)

\(\left|4:x-\frac{1}{2}\right|=3\Leftrightarrow\orbr{\begin{cases}4:x-\frac{1}{2}=3\\4:x-\frac{1}{2}=-3\end{cases}\Leftrightarrow\orbr{\begin{cases}\frac{4}{x}=\frac{7}{2}\\\frac{4}{x}=-\frac{5}{2}\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=\frac{8}{7}\\x=-\frac{8}{5}\end{cases}}}\)

Vì | 4:x - \(\frac{1}{2}\)| = 3 nên ta có 2 trường hợp

Trường hợp 1:

4:x - \(\frac{1}{2}\)= 3

4: x = 3 + \(\frac{1}{2}\)

4: x = \(\frac{7}{2}\)

x = \(\frac{7}{2}\). 4 = 14

Trường hợp 2:

4:x-\(\frac{1}{2}\)= -3

4:x = (-3) + \(\frac{1}{2}\)

4:x = \(\frac{-5}{2}\)

x = \(\frac{-5}{2}\). 4 = -10

Vậy x= 14 hoặc x = -10

Chúc bn học tốt

Trả lời:

\(\left(-\frac{3}{4}\right)^{3x-1}=-\frac{27}{64}\)

\(\Leftrightarrow\left(-\frac{3}{4}\right)^{3x-1}=\left(-\frac{3}{4}\right)^3\)

\(\Rightarrow3x-1=3\)

\(\Leftrightarrow3x=4\)

\(\Leftrightarrow x=\frac{4}{3}\)

mik ko bt

\(\left(x+\frac{1}{2}\right)^2=\frac{4}{25}\)

\(\Rightarrow x+\frac{1}{2}=\pm\sqrt{\frac{4}{25}}\)

\(\Rightarrow\orbr{\begin{cases}x+\frac{1}{2}=\frac{2}{5}\\x+\frac{1}{2}=\frac{-2}{5}\end{cases}}\Rightarrow\orbr{\begin{cases}\frac{-1}{10}\\\frac{-9}{10}\end{cases}}\)

\(\left(x+\frac{1}{2}\right)^2=\frac{4}{25}\)

\(\Leftrightarrow\orbr{\begin{cases}x+\frac{1}{2}=\frac{2}{5}\\x+\frac{1}{2}=-\frac{2}{5}\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-\frac{1}{10}\\x=-\frac{9}{10}\end{cases}}}\)

#H

Trả lời:

76 nha bn

K cho mik ạ, tks

*xin lỗi nãy mình nhầm giờ mới tham khảo được cách làm*

2¹⁰⁰ = (2¹⁰)¹⁰ = 1024¹⁰ = (1024²)⁵ = .....76⁵

Ta thấy 76 nhân với chính nó bao nhiều lần cũng có 2 số tận cùng là 76 nên

2¹⁰⁰ có 2 số tận là 76

Đây nhé

[ 92 - 1/9 - 2/10 - 3/11 - ... - 92/100] : [ 1/45 + 1/50 +1/55 + ... + 1/500]

= (1-1/9 + 1- 2/10 + 1- 3/11...+1 - 92/100) : 1/5 x (1/9 +1/10 + 1/11+...+1/100)

= ( 8/9 + 8/10 + 8/11 + 8/11...+ 8/100) : 1/5 x (1/9 +1/10 + 1/11+...+1/100)

= 8 x (1/9 +1/10 + 1/11+...+1/100) : 1/5 x (1/9 +1/10 + 1/11+...+1/100)

= 8 : 1/5

= 40

giúp mik với cảm ơn nhiều !!!

3.x+3=729

=> 3.(x+1)=729

=> x+1=729 : 3

=> x+1=243

=> x=243-1

=> x=242

c, 18/-5 . -15/20

= 18.(-15)/(-5).20

= 270/100 = 27/10

d, 115/30 : - 5/6

= 115/30 . 6/-5

= 115.6/30.(-5)

= 690/-15

= -46

HỌC TỐT!

Trả lời:

= -46 nhé bn\

~HT~

Kick cho mik nha:33

(7956x4375-725):(3650+4375x7255)

=34806775:31744275

Sấp sỉ  :1,1