Ta có:

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)

\(\Rightarrow\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)

\(\Rightarrow\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)

\(\Rightarrow\frac{1}{1}-\frac{1}{7}=\frac{6}{7}\)

1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42

= 1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 + 1/6x7

= 1/1 + 1/7

= 8/7

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)

\(=\frac{1}{1}-\frac{1}{7}\)

\(=\frac{6}{7}\)

Vậy số HS khối 3 là 3 phần, số HS khối 4 là 4 phần, Số HS khối 5 là 5 phần tương ứng

Tổng số phần bằng nhau: 3+4+5 = 12 (phần)

Số HS khối 3:

864 : 12 x 3 = 216 (HS)

Số HS khối 4:

864 : 12 x 4 = 288 (HS)

Số HS khối 5:

864 : 12 x 5 = 360 (HS)

Đ.số:.....

em cảm ơn thầy ạ

( x - 140) : 7 = 3^ 3 - 2^3. 3

( x - 140) : 7 = 27 - 24

( x - 140) : 7 = 3

 ( x - 140)    = 3.7

( x - 140)     = 21

x                  = 21 + 140

x                  = 161

(x-140):7=27-24

(x-140):7=3

x-140=21

x=161

\(\left(x-140\right)\div7=3^3-2^3.3\)

\(\Rightarrow\left(x-140\right)\div7=27-8.3\)

\(\Rightarrow\left(x-140\right)\div7=27-24\)

\(\Rightarrow\left(x-140\right)\div7=3\)

\(\Rightarrow x\div7=3\)

\(\Rightarrow x=3.7=21\)

\(\Rightarrow x=21+140\)

\(\Rightarrow x=161\)

Ta có \(\frac{1}{3^2}< \frac{1}{2\cdot3}\)

           \(\frac{1}{4^2}< \frac{1}{3\cdot4}\)

           .....................

            \(\frac{1}{100^2}< \frac{1}{99\cdot100}\)

\(\Rightarrow\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< \frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{99\cdot100}\)

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

     \(\Rightarrow\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< \frac{1}{2}-\frac{1}{100}< \frac{1}{2}\)

Vậy \(\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< \frac{1}{2}\)

1/3^2 + 1/4^2 + 1/5^2 + 1/6^2 + ... + 1/100^2 < 1/2

1/3.3 + 1/4.4 + 1/5.5 + 1/6.6 + ... + 1/100.100 < 1/2.3+ 1/3.4 + 1/4 .5 + 1/5.6  + .. + 1/99.100

1/3.3 + 1/4.4 + 1/5.5 + 1/6.6 + ... + 1/100.100 < 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + ... + 1/99 - 1/100

1/3.3 + 1/4.4 + 1/5.5 + 1/6.6 + ... + 1/100.100 < 1/2 - 1/100  suy ra 1/3^2 + 1/4^2 + 1/5^2 + 1/6^2 + ... + 1/100^2 < 1/2

Chúc bn hok tốt 

x là số chắn

A=(-1)^n.3^n

A+3A=4A=1+(-1)^n.3^(n+1) 

với x chẵn

 A= [3^(x+1)+1]/4 vô nghiệm nguyên đề sai

đề bài sai . phai la ...+...+(-3)^x thì mới đúng

ĩ đón nó

Có ai trả lời được ko

a) C1

 \(\dfrac{1}{8}\times\dfrac{5}{6}+\dfrac{5}{6}\times\dfrac{2}{3}=\dfrac{5}{6}\times\left(\dfrac{1}{8}+\dfrac{2}{3}\right)=\dfrac{5}{6}\times\dfrac{19}{24}=\dfrac{95}{144}\)

   C2

\(\dfrac{1}{8}\times\dfrac{5}{6}+\dfrac{5}{6}\times\dfrac{2}{3}=\dfrac{5}{48}+\dfrac{10}{18}=\dfrac{95}{144}\)

b) C1

  \(\dfrac{7}{5}\times\dfrac{3}{4}-\dfrac{1}{2}\times\dfrac{3}{4}=\dfrac{3}{4}\times\left(\dfrac{7}{5}-\dfrac{1}{2}\right)=\dfrac{3}{4}\times\dfrac{9}{10}=\dfrac{27}{40}\)

    C2 

   \(\dfrac{7}{5}\times\dfrac{3}{4}-\dfrac{1}{2}\times\dfrac{3}{4}=\dfrac{21}{20}-\dfrac{3}{8}=\dfrac{27}{40}\)

c) C1

 \(\left(\dfrac{5}{6}+\dfrac{5}{8}\right)\times\dfrac{2}{3}=\dfrac{35}{24}\times\dfrac{2}{3}=\dfrac{35}{36}\)

  C2 

  \(\left(\dfrac{5}{6}+\dfrac{5}{8}\right)\times\dfrac{2}{3}=\left(\dfrac{5}{6}\times\dfrac{2}{3}\right)+\left(\dfrac{5}{8}\times\dfrac{2}{3}\right)=\dfrac{5}{9}+\dfrac{5}{12}=\dfrac{35}{36}\)