S=1/4+1/9+1/16+1/25+1/36+1/49+1/64+1/81=1-1/81=1/81

80/81 là đúng

vô lí vì 2/2 = 1 mà 8/9 < 1

Trả lời

(1-1/4).(1-1/9).(1-1/16).(1-1/25).(1-1/36)

=bước này thì bỏ ngoặc thôi, nên ko ghi lại nha

=1.(-1/4-1/9-1/16-1/25-1/36)

=1.(-900-400-225-144-100/3600)

=1.-1769/3600

=-1769/3600

Chắc sai òi !

\(\left(1-\frac{1}{4}\right).\left(1-\frac{1}{9}\right).\left(1-\frac{1}{16}\right).\left(1-\frac{1}{25}\right).\left(1-\frac{1}{36}\right)\)

\(=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.\frac{24}{25}.\frac{35}{36}\)

\(=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.\frac{4.6}{5.5}.\frac{5.7}{6.6}\)

\(=\frac{1.2.3.4.5}{2.3.4.5.6}.\frac{3.4.5.6.7}{2.3.4.5.6}\)

\(=\frac{1}{6}.\frac{7}{2}\)

\(=\frac{7}{12}\)

\(\frac{2}{12}\)

\(\frac{7}{12}\)

mình nhầm

7/12 là đúng nhé

Tacó cho công thức tổng quát: A² - B² = (A+B).(A-B) 
A = (1-1/4)x(1-1/9)x(1-1/16)x(1-1/25)x(1-1/3... 
= (1+1/2) x (1-1/2) x (1+1/3) x (1-1/3) x...x (1+1/n) x (1-1/n) 
= (1+1/2) x (1+1/3) x (1+1/4) x ... x [1 + 1/(n-1) ] x (1 + 1/n) 
x (1-1/2) x (1-1/3) x (1-1/4) x ... x [1 - 1/(n-1) ] x (1 - 1/n) 
= 3/2 x 4/3 x 5/4 x ... x [ n/(n-1) ] x [ (n+1)/n ] 
x 1/2 x 2/3 x 3/4 x ... x [ (n-2)/(n-1) ] x [ (n-1)/n] 
               Vậy dãy A là:
A = 1/2 x 2/3 x 3/2 x 3/4 x 4/3 x 4/5 x 5/4 x .... x [ (n-2)x(n-1) ] x [ (n-1)/n] x [ n/(n-1)] x [ (n+1)/n] 
= 1/2 x 1 x 1 x 1 x ... x 1 x [(n+1)/n] 

giai bang cach lop 5

lời giải luôn nhé

\(\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times\left(1-\frac{1}{16}\right)\times\left(1-\frac{1}{25}\right)\times\left(1-\frac{1}{36}\right)\)

\(=\)\(\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times\frac{24}{25}\times\frac{35}{36}\)

\(=\)\(\frac{3\times8\times15\times24\times35}{4\times9\times16\times25\times36}\)

\(=\)\(\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\frac{\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}3\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times4\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times2\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times5\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times3\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times6\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times4\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times5\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times7}{4\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times3\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times3\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times8\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times2\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times5\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times5\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times6\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\times6}\)

\(=\)\(\frac{7\text{​​}\text{​​}\text{​​}\times4}{8\times6}\)

\(=\)\(\frac{7\times4}{4\times2\times6}\)

\(=\)\(\frac{7}{2\times6}\)

\(=\)\(\frac{7}{12}\)

A=1/2²+1/3²+...+1/9²

Ta có:1/2²>1/2.3,1/3²>1/3.4,...,1/9²>1/9.10

⇒A>1/2.3+1/3.4+...+1/9.10

A>1/2-1/3+1/3-1/4+...+1/9-1/10

A>1/2-1/10

A>2/5(đpcm)

Ta có: A = 1/4 + 1/9 + 1/16 + 1/25 +1/36 + 1/49 + 1/64 + 1/81

Vì 1/2²>1/2.3,1/3²>1/3.4,...,1/9²>1/9.10

=>A>1/2.3+1/3.4+...+1/9.10

=>A>1/2-1/3+1/3-1/4+...+1/9-1/10

=>A>1/2-1/10

=>A>2/5

Giải:

\(A=\dfrac{1}{4}+\dfrac{1}{9}+\dfrac{1}{16}+\dfrac{1}{25}+\dfrac{1}{36}+\dfrac{1}{49}+\dfrac{1}{64}+\dfrac{1}{81}\) 

\(A=\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2} +\dfrac{1}{5^2}+\dfrac{1}{6^2}+\dfrac{1}{7^2}+\dfrac{1}{8^2}+\dfrac{1}{9^2}\) 

Ta có:

\(\dfrac{1}{2^2}=\dfrac{1}{2.2}>\dfrac{1}{2.3}\) 

\(\dfrac{1}{3^2}=\dfrac{1}{3.3}>\dfrac{1}{3.4}\) 

\(\dfrac{1}{4^2}=\dfrac{1}{4.4}>\dfrac{1}{4.5}\) 

\(\dfrac{1}{5^2}=\dfrac{1}{5.5}>\dfrac{1}{5.6}\) 

\(\dfrac{1}{6^2}=\dfrac{1}{6.6}>\dfrac{1}{6.7}\) 

\(\dfrac{1}{7^2}=\dfrac{1}{7.7}>\dfrac{1}{7.8}\) 

\(\dfrac{1}{8^2}=\dfrac{1}{8.8}>\dfrac{1}{8.9}\) 

\(\dfrac{1}{9^2}=\dfrac{1}{9.9}>\dfrac{1}{9.10}\) 

\(\Rightarrow A>\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10}\) 

\(\Rightarrow A>\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\)

\(\Rightarrow A>\dfrac{1}{2}-\dfrac{1}{10}\) 

\(\Rightarrow A>\dfrac{2}{5}\left(đpcm\right)\) 

Chúc bạn học tốt!

>1/4+1/4+1/16+1/16+1/16

=2/4+3/16=11/16=66/96<80/96=5/6

vậy A<5/6