`1/3+1/4+2/5+2/3+3/4+3/5`

`=(1/3+2/3)+(1/4+3/4)+(2/5+3/5)`

`=1+1+1`

`=3`

giúp mình với đi ạ :{

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Đặt \(A=\dfrac{1}{3}+\dfrac{1}{3^3}+\dfrac{1}{3^5}+...+\dfrac{1}{3^{47}}+\dfrac{1}{3^{49}}+\dfrac{1}{3^{51}}\)

Và \(B=\dfrac{1}{3^2}+\dfrac{1}{3^4}+\dfrac{1}{3^6}+...+\dfrac{1}{3^{46}}+\dfrac{1}{3^{48}}+\dfrac{1}{3^{50}}\)

Ta có:

\(9A=3+\dfrac{1}{3}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{45}}+\dfrac{1}{3^{47}}+\dfrac{1}{3^{49}}\)

\(9A-A=\left(3+\dfrac{1}{3}+...+\dfrac{1}{3^{47}}+\dfrac{1}{3^{49}}\right)-\left(\dfrac{1}{3}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{49}}+\dfrac{1}{3^{51}}\right)\)

\(8A=3-\dfrac{1}{3^{51}}\)

\(A=\dfrac{3-\dfrac{1}{3^{51}}}{8}\)

\(9B=1+\dfrac{1}{3^2}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{44}}+\dfrac{1}{3^{46}}+\dfrac{1}{3^{48}}\)

\(9B-B=\left(1+\dfrac{1}{3^2}+...+\dfrac{1}{3^{46}}+\dfrac{1}{3^{48}}\right)-\left(\dfrac{1}{3^2}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{48}}+\dfrac{1}{3^{50}}\right)\)

\(8B=1-\dfrac{1}{3^{50}}\)

\(B=\dfrac{1-\dfrac{1}{3^{50}}}{8}\)

Suy ra

\(-\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^{50}}-\dfrac{1}{3^{51}}=B-A=\dfrac{1-\dfrac{1}{3^{50}}}{8}-\dfrac{3-\dfrac{1}{3^{51}}}{8}\)

\(=\dfrac{\left(1-\dfrac{1}{3^{50}}\right)-\left(3-\dfrac{1}{3^{51}}\right)}{8}=\dfrac{-2-\dfrac{1}{3^{50}}+\dfrac{1}{3^{51}}}{8}=\dfrac{-2+\dfrac{-3^{51}+3^{50}}{3^{101}}}{8}\)

\(=\dfrac{-2+\dfrac{3^{50}\left(-3+1\right)}{3^{101}}}{8}=\dfrac{-2-\dfrac{2}{3^{51}}}{8}=-\dfrac{2\left(1+\dfrac{1}{3^{51}}\right)}{8}=-\dfrac{1+\dfrac{1}{3^{51}}}{4}\)

đề b là j vậy

tui cần bài đó thôi

Chứng minh : A =1+1/2+1/3+...+1/100 không phải là số tự nhiên

=> A <1

Ta có:

A=1+1/2+1/3+...+1/100 <1

=>A=1+1/2+1/3+..+1/100<1/1.2+1/2.3+...+1/99.100

A= 1+1/2+1/3+..+1/100< 1-1/2+1/2-1/3+...+1/99-1/100

A=1+1/2+1/3+..+1/100<1-1/100

A=1+1/2+1/3+..+1/100<99/100

Vì 99/100 <1

nên A=1+1/2+1/3+..+1/100<1

=> A=1+1/2+1/3+..+1/100 không phải là số tự nhiên.

( \(\dfrac{1}{1}\)+\(\dfrac{1}{2}\)) :( \(\dfrac{1}{1}\)+\(\dfrac{1}{3}\)) : ( \(\dfrac{1}{ }1\)+\(\dfrac{1}{4}\))= \(\dfrac{2}{1}\):\(\dfrac{3}{1}\):\(\dfrac{4}{1}\)=2:3:4=0.16666666666

   \(\left(1+\dfrac{1}{2}\right)\div\left(1+\dfrac{1}{3}\right)\div\left(1+\dfrac{1}{4}\right)\)

\(=\dfrac{3}{2}\div\dfrac{4}{3}\div\dfrac{5}{4}\)

\(=\dfrac{3}{2}\times\dfrac{3}{4}\times\dfrac{4}{5}=\dfrac{9}{8}\times\dfrac{4}{5}=\dfrac{9}{10}\)

Mà lớp 4 mk đã học 0. hay 1. gì gì đó đâu ta

\(1\dfrac{1}{9}\)

=4/9 x 5/2=10/9

\(\dfrac{4}{3}\times\dfrac{1}{3}\times\dfrac{5}{2}=\dfrac{10}{9}\)

1 3/4 - x = 4/5  

7/4 - x = 4/5

x = 7/4 - 4/5

x = 19/20

\(=>\dfrac{7}{4}-x=\dfrac{4}{5}\)

\(=>x=\dfrac{7}{4}-\dfrac{4}{5}=\dfrac{35}{20}-\dfrac{16}{20}=\dfrac{19}{20}\)

Sửa đề: 1/2*1/3+1/3*1/4+...+1/19*1/20

=1/2-1/3+1/3-1/4+...+1/19-1/20

=1/2-1/20=10/20-1/20=9/20

X x 3 1/3= 3 1/3 : 4 1/4

X x 10/3=10/3:17/4

X x 10/3= 10/3:17/4

X x 10/3= 40/51

X           = 40/51:10/3

X           = 120/510

X           = 12/51

X           = 4/17

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\(\frac{5}{3}-\frac{1}{4}+\frac{1}{3}-\frac{3}{4}\)

\(=\frac{5}{3}+\frac{-1}{4}+\frac{1}{3}+\frac{-3}{4}\)

\(=\left(\frac{5}{3}+\frac{1}{3}\right)+\left(\frac{-1}{4}+\frac{-3}{4}\right)\)

\(=\frac{6}{3}+\frac{-4}{4}\)

\(=2+\left(-1\right)\)

\(=1\)

`(-3/4)+(-1/4)+2/7+5/7+3/5`

`=[(-3/4)+(-1/4)]+(2/7+5/7)+3/5`

`=-4/4+7/7+3/5`

`=-1+1+3/5`

`=0+3/5`

`=3/5`

-3/4 + -1/4 + 2/7  + 5/7 + 3/5 

= (-3/4 + -1/4) + (2/7  + 5/7) + 3/5

= (-1 + 1) + 3/5

= 0 + 3/5

= 0