3/n . n/3 = 3.n/n.3 = 1

3/n.n/3 = 3n/3n =1 

bai toan: 21π²=?

π≈3.1416

π²≈3.1416×3.1416≈9.8696

21×π²≈21×9.8696≈207.2616

vay21π²≈207.26

1+1=

Bài 1)

Ta có:

A = \(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+\dfrac{1}{5^2}+\dfrac{1}{6^2}+\dfrac{1}{7^2}+\dfrac{1}{8^2}\)

A < \(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}\)

A < \(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}\)

A < \(1-\dfrac{1}{8}\) = \(\dfrac{7}{8}\) < 1

Vậy A < 1

Bài 2)

Ta thấy:

\(\dfrac{2011}{2012+2013}< \dfrac{2011}{2012};\dfrac{2012}{2012+2013}< \dfrac{2012}{2013}\)

\(\Rightarrow\) \(\dfrac{2011}{2012+2013}+\dfrac{2012}{2012+2013}< \dfrac{2011}{2012}+\dfrac{2012}{2013}\)

\(\Rightarrow\) \(\dfrac{2011+2012}{2012+2013}< \dfrac{2011}{2012}+\dfrac{2012}{2013}\)

\(\Rightarrow\) A < B

Bài 3)

Ta có:

B = \(\left(1-\dfrac{1}{1}\right)\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{4}\right)......\left(1-\dfrac{1}{20}\right)\)

= \(0.\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)......\left(1-\dfrac{1}{20}\right)\)

= 0

Bài 3)

Ta có:

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

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

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

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

\(\Rightarrow\) A = 2 - \(\dfrac{1}{2^{2012}}\) = \(\dfrac{2^{2013}-1}{2^{2012}}\)

Bài 5)

\(\pi\) + 5 \(⋮\) \(\pi\) - 2

\(\Leftrightarrow\) \(\pi\) - 2 + 7 \(⋮\) \(\pi\) - 2

\(\Leftrightarrow\) 7 \(⋮\) \(\pi\) - 2 (vì \(\pi\) - 2 \(⋮\) \(\pi\) - 2)

\(\Leftrightarrow\) \(\pi\) - 2 \(\in\) Ư₍₇₎

\(\Leftrightarrow\) \(\pi\) - 2 \(\in\) \(\left\{\pm1;\pm7\right\}\)

\(\Leftrightarrow\) \(\pi\) \(\in\) \(\left\{1;3;-5;9\right\}\)

ok , kb luôn

cong thuc tinh hinh tron

a)\(3.5^2-16:2^2\)

=\(3.25-16:4\)

=\(75-4=71\)

b)\(2^3.17-2^3.14\)

=\(8.17-8.14\)

\(=8\left(17-14\right)\)

\(=8.3=24\)

c)\(15.141+59.15\)

=\(15\left(141+59\right)\)

\(=15.200\)=3000

d)17.85+15.17-120

\(=17\left(85+15\right)-120\)

=\(17.100-120\)

=\(170-120=50\)

e)\(20+[30-\left(5-1\right)^2]\)

\(=20+[30-\left(4\right)^2]\)

\(=20+\left(30-16\right)\)

\(=20+14=34\)

Bạn làm đúng ko vậy 

\(\frac{2^3.3^3.5^3.7.8}{3.2^4.5^3.14}=\frac{2^3.3^3.5^3.7.2^3}{3.2^4.5^3.2.7}\)

\(=\frac{2^6.3^3.5^3.7}{2^5.3.5^3.7}=\frac{2.3^2.1.1}{1.1.1.1}=2.3^2\)

\(=2.9=18\)

\(\frac{2^3.3^3.5^3.7.8}{3.2^4.5^3.14}=\frac{1.3^2.1.1.8}{1.2.1.2}=\frac{3.3.4}{2.1}=\frac{3.3.2}{1}=18\)

\(\frac{2^3.3^3.5^3.7.8}{3.2^4.5^3.14}\)mk viết như vầy bn cố gắng hiểu nhé:.

2³.3³.5³.7.8/ 3.2⁴.5³.14

= 2³.3³.5³.7.8/3.2⁴.5³.7.2

=2³.3³.5³.8/3.2⁴.5³.2

=2³.3³.5³.2³/2⁴.2.5³

= 2³.2³.3³.5³/ 2⁴.2.5³

= 2⁶. 3³.5³/ 2⁵. 5³

= 2⁵.2.3³.5³/2⁵.5³

= 2.3³/1

^{= 2. 27/1}

^{= 54/1 = 54}

^{Thế nha bn, chúc bn học tốt!}

/ là phân số hả bạn

\(\frac{2^3.3^3.5^3.7.8}{3.2^4.5^3.14}=\frac{2^3.3^3.5^3.7.2^3}{3.2^4.5^3.2.7}\)

                            \(=\frac{2^6.3^3.5^3.7}{2^5.3.5^3.7}\)

                              \(=\frac{\left(2^5.3.5^3.7\right).2.3^2}{2^5.3.5^3.7}\)

                                \(=2.9=18\)

\(=\frac{3.8}{2.2}=\frac{24}{4}=6\)

B/  2³3×3²×5³×7×8

3×2³×2 ×5³×7×2

=3²×8

2×2

=18