A)17/5.-31/125.1/2.10/17.-1/2 mũ 3

=(17/5.10/17).(1/2.-1/6).-31/125

=2.(-1/12).(-31/125)

=-1/6.(-31/125)

=31/125

B)(11/4.-5/9.4/9.11/4).8/33

=(11/4.(-5/9.4/9)).8/33

=(11/4.(-1)).8/33

=(-11/4).8/33

=-2/3

C)(135/21 +45/123 - 55/434).(-5/12 + 1/4 + 1/6

=(135/21 +45/123 - 55/434).(5/12+3/12+2/12)

=(135/21 +45/123 - 55/434).0

= 0

D) 132/111. (1 /2 + 1/3 + 7/6)

=12.(3/6+2/6+7/6)

= 12.7/3

= 28

E)1/5.1/6 + 1/6.1/7 + 1/7.1/8 + 1/8 . 1/9 + 1/9.9/10

=1/5.6+1/6.7+1/7.8+1/8.9+(1/9.9/10)

=1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/10

=1/5-1/10

= 1/10

Mình ko biết làm câu F thông cảm nhé

Sai thì bình luận cho mình biết với nhé

Bài 1.

\(a,\left(2^4\cdot3\cdot5^2\right):\left\{450:\left[450-\left(4\cdot5^3-2^3\cdot5^2\right)\right]\right\}\)

\(=\left(16\cdot3\cdot25\right):\left\{450:\left[450- \left(4\cdot125-8\cdot25\right)\right]\right\}\)

\(=\left(48\cdot25\right):\left\{450:\left[450-\left(500-200\right)\right]\right\}\)

\(=1200:\left[450:\left(450-300\right)\right]\)

\(=1200:\left(450:150\right)\)

\(=1200:3\)

\(=400\)

\(---\)

\(b,3^3\cdot5^2-20\left\{90-\left[164-2\cdot\left(7^8:7^6+7^0\right)\right]\right\}\)

\(=27\cdot25-20\left\{90-\left[164-2\cdot\left(7^2+1\right)\right]\right\}\)

\(=675-20\left\{90-\left[164-2\cdot\left(49+1\right)\right]\right\}\)

\(=675-20\left[90-\left(164-2\cdot50\right)\right]\)

\(=675-20\left[90-\left(164-100\right)\right]\)

\(=675-20\left(90-64\right)\)

\(=675-20\cdot26\)

\(=675-520\)

\(=155\)

\(---\)

\(c,\left[\left(18^7:18^6-17\right)\cdot2022-1986\right]\cdot5\cdot1^{2022}-13^2\cdot2020^0\)

\(=\left[\left(18-17\right)\cdot2022-1986\right]\cdot5\cdot1-169\cdot1\)

\(=\left(1\cdot2022-1986\right)\cdot5-169\)

\(=\left(2022-1986\right)\cdot5-169\)

\(=36\cdot5-169\)

\(=180-169\)

\(=11\)

Bài 2.

\(a) (2^x+1)^2+3\cdot(2^2+1)=2^2\cdot10\\\Rightarrow (2^x+1)^2+3\cdot(4+1)=4\cdot10\\\Rightarrow (2^x+1)^2+3\cdot5=40\\\Rightarrow (2^x+1)^2+15=40\\\Rightarrow (2^x+1)^2=40-15\\\Rightarrow (2^x+1)^2=25\\\Rightarrow (2^x+1)^2= (\pm 5)^2\\\Rightarrow \left[\begin{array}{} 2^x+1=5\\ 2^x+1=-5 \end{array} \right.\\ \Rightarrow \left[\begin{array}{} 2^x=4\\ 2^x=-6 (vô.lí) \end{array} \right. \\ \Rightarrow 2^x=2^2\\\Rightarrow x=2\)

Vậy \(x=2\).

\(---\)

\(b)3\cdot(x-7)+2\cdot(x+5)=41\\\Rightarrow 3\cdot x+3\cdot(-7)+2\cdot x+2\cdot5=41\\\Rightarrow 3x-21+2x+10=41\\\Rightarrow (3x+2x)+(-21+10)=41\\\Rightarrow 5x-11=41\\\Rightarrow 5x=41+11\\\Rightarrow 5x=52\\\Rightarrow x=\dfrac{52}{5}\)

Vậy \(x=\dfrac{52}{5}\).

\(Toru\)

=-1/2.3-1/3.4-1/4.5-1/5.6

=-(1/2.3+1/3.4+1/4.5+1/5.6)

=-(1/2-1/3+1/3-1/4+1/5-1/6)

=-(1/2-1/6)

=1/6-1/2=-1/3

giải giùm e vs ạ

A) bạn xem lại đề ạ

B) 1/2 + 1/6 + 1/ 12 + 1/ 20 + ...+ 1/ 9900
=1/2+1/6+1/12+...+1/9900
=1/1.2+1/2.3+1/3.4+...+1/99.100
=1/1-1/2+1/2-1/3+...+1/99-1/100
=1/1-1/100
=99/100
C) Biến đổi tử số và mẫu số ta có

- Tử số: 20,2 x 5,1 - 30,3 x 3,4 + 14,58
          = 103,02 - 103,02 + 14,58
          = 14,58
- Mẫu số: 14,58 x 460 + 7,29 x 540 x 2
          = 14,58 x 460 + 14,58 x 540
          = 14,58 x (460 + 540)
          = 14,58 x 1000
          = 14580

Thay vào ta có: = 14,58 : 14580
                         = 0,001
Vậy 20.2*5.1-30.3*3.4+14.56/ 14.58*460+7.29 *540*2 = 0,001.

\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{18}+\frac{1}{54}+\frac{1}{162}\)

\(\Rightarrow A=\frac{1}{2}\left(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}\right)\)

Gọi  \(B=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}\)

\(\Rightarrow\frac{1}{3}B=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)

\(\Rightarrow B-\frac{1}{3}B=1-\frac{1}{243}\)

\(\Rightarrow\frac{2}{3}B=\frac{242}{243}\)

\(\Rightarrow B=\frac{121}{81}\)

Suy ra  \(A=\frac{1}{2}B=\frac{1}{2}.\frac{121}{81}=\frac{121}{162}\)

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{9900}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)

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

\(=1-\frac{1}{100}\)

\(=\frac{99}{100}\)