a (1/6 + 1/10 + 1/15) : (1/6 + 1/10 - 1/15)

= ( 5/30 + 3/30 + 2/30) : (5/30 + 3/30 - 2/30)

= 1/3 : 1/6 = 1/3 x 6/1 = 6/3 = 2

b (1/2 - 1/3 + 1/4 - 1/5) : (1/4 - 1/5)

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

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

a)  

(1/6+1/10+1/15) : (1/6+1/10-1/15)

= (1/6+1/10): (1/6+1/10)

= 4/15:4/15

=1

~Hy

b)

(1/2-1/3 +1/4-1/5): (1/4-1/5)

= (1/2-1/3) :(1/4-1/5)

= 1/6:1

=1/6

~Hy

Bạn Kiên giải đúng nhưng chưa rõ nên mình giải lại.

\(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{202}{201}\)

\(=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{202}{201}\)

\(=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{x\left(x+1\right)}=\frac{202}{201}\)

\(=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{\left(x+1\right)}\right)=\frac{202}{201}\)

\(=2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{202}{201}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{\left(x+1\right)}=\frac{202}{201}:2=\frac{202}{402}\)

\(\Rightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{202}{402}=-\frac{1}{402}=\frac{-1}{402}=\frac{1}{-402}\)

\(\Rightarrow\frac{1}{x+1}=\hept{\begin{cases}\frac{-1}{402}\\\frac{1}{-402}\end{cases}}\Rightarrow x+1=\hept{\begin{cases}402\\-402\end{cases}}\Rightarrow\hept{\begin{cases}x=402-1\\x=\left(-402\right)-1\end{cases}}\Rightarrow x=\hept{\begin{cases}401\\-403\end{cases}}\)

\(\Rightarrow A=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x.\left(x+1\right)}=\frac{202}{201}\)\(\Rightarrow A=2.\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x.\left(x+1\right)}\right)=\frac{202}{201}\)

\(\Rightarrow A=2.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x.\left(x+1\right)}\right)=\frac{202}{201}\)

\(\Rightarrow A=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{202}{201}\)

\(\Rightarrow A=2.\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{202}{201}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{202}{402}\)

\(\Rightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{202}{402}=\frac{-1}{402}\)

\(\Rightarrow\frac{1}{x+1}=\frac{1}{-402}\)

\(\Rightarrow x+1=-402\)

\(\Rightarrow x=-403\)

\(A=\frac{15\times3^{11}+4\times27^4}{9^7}\)

\(A=\frac{15\times177147+4\times531441}{4782969}\)

\(A=\frac{2657205+2125764}{4782969}\)

\(A=\frac{47829969}{47829969}=1\)

Tự nhiên phần Σ của tớ bị lỗi nên tớ tính tử số rồi tính mẫu nhé :

Tử số của A :

15 x 3¹¹ + 4 x 27⁴

= 5 x 3¹² + 4 x 3¹²

= 3¹² x ( 5 + 4 ) 

= 3¹² x 9 

= 3¹² x 3²

= 3¹⁴

Mẫu số của A :

97 = (3²)⁷ = 3^{2 x 7} = 3¹⁴

Vậy A = 3¹⁴ : 3¹⁴ = 1

\(B=\frac{\frac{7}{12}+\frac{5}{6}-1}{5-\frac{3}{4}+\frac{1}{3}}\)

\(B=\frac{\frac{7}{12}+\frac{10}{12}-\frac{12}{12}}{\frac{60}{12}-\frac{9}{12}+\frac{4}{12}}\)

\(B=\frac{\frac{5}{12}}{\frac{55}{12}}\)

\(B=\frac{1}{11}\)

(1-1/3).(1-1/6).(1-1/10)...(1-1/780) (ko có dấu "...") 
Giải: (1-1/3).(1-1/6).(1-1/10)...(1-1/780) 
= 2/3 . 5/6....779/780 
= 4/6 . 10/12.....1558/1560 
= 1.4 . 2.5 .... 38.41/ 2.3 . 3. 4. .....39.40 
= ( 1.2.3....38).(4.5....41)/(2.3.4....39)(3... 
triệt tiêu xong còn 41/39.3= 41/117 
ĐS = 41/117

k cho mh nha bạn

D=2/3.5/6.9/10.....779/780

  =       

\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.....\frac{9999}{10000}\)

\(A=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{99.101}{100.100}\)

\(A=\frac{\left(1.2.3.....99\right).\left(3.4.5.....101\right)}{\left(2.3.4.....100\right).\left(2.3.4.....100\right)}\)

\(A=\frac{1.101}{2.100}=\frac{101}{200}\)

\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}......\frac{9999}{10000}\)

\(A=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{99.101}{100.100}\)

\(A=\frac{1.2.3.4.....99}{2.3.4.5.....100}.\frac{3.4.5.6.....101}{2.3.4.5.....100}\)

\(A=\frac{1}{100}.\frac{101}{2}\)

\(A=\frac{101}{200}\)

\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}...\frac{9999}{10000}\)

\(A=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}...\frac{99.101}{100.100}\)

\(A=\frac{1.2...99}{2.3...100}.\frac{3.5...101}{2.3...100}\)

\(A=\frac{1}{100}.\frac{101}{2}\)

\(=\frac{101}{200}\)

\(B=\left(1-\frac{1}{3}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{10}\right)\left(1-\frac{1}{15}\right)...\left(1-\frac{1}{780}\right)\)

\(B=\frac{2}{3}.\frac{5}{6}.\frac{9}{10}.\frac{14}{15}...\frac{779}{780}\)

\(B=\frac{4}{6}.\frac{10}{12}.\frac{18}{20}....\frac{1558}{1560}\)

\(B=\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}...\frac{38.41}{39.40}\)

\(B=\frac{1.2.3...38}{2.3...39}.\frac{4.5...41}{3.4...40}\)

\(B=\frac{1}{39}.\frac{41}{3}\)

\(B=\frac{41}{117}\)

\(3^4.5^4-\left(15^2+1\right)\left(15^2-1\right)=\left(3.5\right)^4-\left(15^4-1\right)\)

\(=15^4-15^4+1=1\)

a) 25/42 - 20/63 = 5/18

b) ( 9/50 - 13/75 - 1/6 ) : ( -1/2 )² = -16/25

c) ( 2/15 - 2/65 - 4/39 ) : ( 1/2 - 1/3 )² = 0

kick và kết bạn với mình nha