qua de dang nhe

S=1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+...+1/(1+2+3+4+...+10)

S=1/(2*3/2)+1/(3*4/2)+1/(4*5/2)+...+1/(10*11/2)

S=2(1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+...+1/(10*11)

S=2(1/2-1/3+1/3-1/4+1/4-1/5+...+1/10-1/11)

S=2(1/2-1/11)

S=2*9/22

S=9/11

nho k cho minh voi nha

\(S=\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+...+10}\)

\(S=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{55}\)

\(S=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{110}\)

\(S=2\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{110}\right)\)

\(S=2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{10.11}\right)\)

\(S=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}\right)\)

\(S=2\left(\frac{1}{2}-\frac{1}{11}\right)\)

\(S=2.\frac{9}{22}\)

\(S=\frac{9}{11}\)

Ta có:

\(\frac{5}{1\cdot7}+\frac{5}{7\cdot13}+\frac{5}{13\cdot19}+...+\frac{5}{91\cdot97}\)

= \(5\cdot\frac{1}{6}\cdot\left(\frac{6}{1\cdot7}+\frac{6}{7\cdot13}+\frac{6}{13\cdot19}+...+\frac{6}{91\cdot97}\right)\)

= \(\frac{5}{6}\cdot\left(1-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+\frac{1}{13}-\frac{1}{19}+...+\frac{1}{91}-\frac{1}{97}\right)\)

= \(\frac{5}{6}\cdot\left(1-\frac{1}{97}\right)\)

= \(\frac{5}{6}\cdot\frac{96}{97}\)

= \(\frac{80}{97}\)

5/1.7 + 5/7.13 + 5/13.19 + ... + 5/91.97

= 5/6.(1 - 1/7 + 1/7 - 1/13 + 1/13 - 1/19 + ... + 1/91 - 1/97)

= 5/6.(1 - 1/97)

= 5/6.96/97

= 80/97

5/1.7+5/7.13+5/13.19+....+5/91.97

=5.(1/1.7+1/7.13+1/13.19+...+1/91.97)

=5.1/6.(6/1.7+6/7.13+6/13.19+....+6/91.97)

=5/6.(1-1/7+1/7-1/13+1/13-1/19+.....+1/91-1/97)

=5/6.(1-1/97)

=5/6.96/97

=80/97

Hok tốt

\(\frac{4}{x}\) \(=\frac{1}{5}\)

Ta có :

\(\frac{4}{x}\) \(=\frac{4}{20}\)

=> \(x=20\)

#Ninh Nguyễn

x.1=4.5

x.1=20

x=20:1

x=20

x.1 = 4.5

x.1 = 20

x    = 20

Vậy x = 20

có nghĩa là lấy 3/2 nhân vs từng số hạng trong ngoặc nó sẽ ra là như vậy

 CÁC BẠN GIẢI RA LẦN LƯỢT NHÉ CÓ CẢ LỜI GIẢI VÀ PHÉP TINH NHE

1/1/3+3/1/4+4/1/5

=4/3+13/4+21/5

=?

2/5+3/5=1

 K mk nha!!!!! 

2/5+3/5=5/5=1.
k nha tớ kb rồi đó.

\(\frac{2}{5}+\frac{3}{5}=1\)

\(\frac{2}{3}+\frac{1}{3}:x=\frac{3}{5}\)

\(\Rightarrow\frac{1}{3}:x=\frac{3}{5}-\frac{2}{3}\)

\(\Rightarrow\frac{1}{3}:x=\frac{9}{15}-\frac{10}{15}\)

\(\Rightarrow\frac{1}{3}:x=\frac{-1}{15}\)

\(\Rightarrow x=\frac{1}{3}:\frac{-1}{15}\)

\(\Rightarrow x=\frac{1}{3}.\frac{-15}{1}\)

\(\Rightarrow x=-5\)

Vậy \(x=-5\)