ai nhanh nhất mình k cho

Bài 1:

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

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

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

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

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

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

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

Bài 2 :

2)  Tử số = 11 x 13 x 15 + 3 x 3 x 3 x 11 x 13 x 15 + 5 x 5 x 5 x 11 x 13 x 15 + 9 x 9 x 9 x 11 x 13 x 15

= (1 + 3 x 3 x 3 + 5 x 5 x 5 + 9 x 9 x9) x 11 x 13 x 15 = (1+27+125+ 729) x 11 x 13 x 15

Mẫu số =  11 x 13 x 17 + 3 x 3 x 3 x 13 x 15 x 19  + 5 x 5 x 5 x 13 x 15 x 17 + 9 x 9 x 9 x 13 x 15 x 17 lớn hơn 11 x 13 x 15 + 3 x 3 x 3 x 13 x 15 x 17 + 5 x 5 x 5 x 13 x 15 x 17 + 9 x 9 x 9 x 13 x 15 x 17  

=  (1 + 3 x 3 x 3 + 5 x 5 x 5 + 9 x 9 x9) 13 x 15 x  17 = (1+27+125+729) x 13 x 15 x 17 

\(\Rightarrow A< \frac{\left(1+27+125+729\right)\times11\times13\times15}{\left(1+27+125+729\right)\times13\times15\times17}\)

\(=\frac{11}{17}\)

\(=\frac{1111}{1717}=B\)

Vậy \(A=B\)

mình đâu biết

a, 24^10 < 3^30 + 4^30 + 5^30

b, 2^100 < 5^50 < 3^75.

1)\(A=\frac{1}{3}+\frac{1}{6}+...+\frac{1}{55}=2\left(\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}\right)=2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}\right)=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\right)=2.\left(\frac{1}{2}-\frac{1}{11}\right)=\frac{9}{11}\)

2) Tử số = 11 x 13 x 15 + 3 x 3 x 3 x 11 x 13 x 15 + 5 x 5 x 5 x 11 x 13 x 15 + 9 x 9 x 9 x 11 x 13 x 15

= (1 + 3 x 3 x 3 + 5 x 5 x 5 + 9 x 9 x9) x 11 x 13 x 15 = (1+27+125+ 729) x 11 x 13 x 15

Mẫu số =  11 x 13 x 17 + 3 x 3 x 3 x 13 x 15 x 19  + 5 x 5 x 5 x 13 x 15 x 17 + 9 x 9 x 9 x 13 x 15 x 17 

lớn hơn 11 x 13 x 15 + 3 x 3 x 3 x 13 x 15 x 17 + 5 x 5 x 5 x 13 x 15 x 17 + 9 x 9 x 9 x 13 x 15 x 17 

=  (1 + 3 x 3 x 3 + 5 x 5 x 5 + 9 x 9 x9) 13 x 15 x  17 = (1+27+125+729) x 13 x 15 x 17

=> \(A

giải giùm mình bài này vớC= (67/111+2/33-15/117)x(1/3-1/4-1/12)

\(3^{40}=\left(3^4\right)^{10}=81^{10}\)

\(4^{30}=\left(4^3\right)^{10}=64^{10}\)

Vì \(81>64\)

`-> 81^10 > 64^10`

`-> 3^40 > 4^30`

`----`

`2^75=(2^3)^25=8^25`

`3^50=(3^2)^25=9^25`

Vì `9>8`

`-> 9^25 > 8^25`

`-> 3^50 > 2^75`.

a: 3^40=81^10

4^30=64^10

=>3^40>4^30

b: 2^75=8^25

3^50=9^25

=>2^75<3^50

a/ \(2^{100}=\left(2^3\right)^{100}=8^{100}>8^{30}\)

b/ \(3^{75}=\left(3^3\right)^{25}=27^{25}\)

\(4^{50}=\left(4^2\right)^{25}=16^{25}\)

\(\Rightarrow3^{75}>4^{50}\)

c/ \(9^{199}=\left(3^2\right)^{199}=3^{398}\)

\(27^{121}=\left(3^3\right)^{121}=3^{363}\)

\(\Rightarrow9^{199}>27^{121}\)

d/ \(26^{38}>16^{38}=\left(2^4\right)^{38}=2^{152}\)

\(64^{25}=\left(2^6\right)^{25}=2^{150}\)

\(\Rightarrow26^{38}>64^{25}\)

a, (-2)⁴ và (-4)²

    (4)² và (-4)²

 Vậy (-2)⁴ > (-4)²

b, (-2)³⁰⁰ và (-3)²⁰⁰

    (-8)¹⁰⁰ và (-9)¹⁰⁰

 Vậy (-2)³⁰⁰ > (-3)²⁰⁰

c, (-2)⁷⁵ và (-9)²⁵

    (-8)²⁵ và (-9)²⁵

 Vậy (-2)⁷⁵ > (-9)²⁵

Tk mk nha

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Thank you very much

a) 27/82 < 26/75 ( 2025/6250 < 2132\6250)

b) -49/78 > 64/ -95 ( - 3136/7410 > -4992/7410)

c) ta có: \(A=\frac{54.107-53}{53.107}=\frac{53.107+(107-53)}{53.107+54}=\frac{53.107+54}{53.107+54}=1\)

\(B=\frac{135.269-133}{134.269+135}=\frac{134.269+\left(269-133\right)}{134.269+135}=\frac{134.269+136}{134.269+135}>1\)

\(\Rightarrow A< B\)

d) ta có: \(A=\frac{3^{10}+1}{3^9+1}=\frac{3.\left(3^9+1\right)-2}{3^9+1}=\frac{3.\left(3^9+1\right)}{3^9+1}-\frac{2}{3^9+1}=3-\frac{2}{3^9+1}\)

\(B=\frac{3^9+1}{3^8+1}=\frac{3.\left(3^8+1\right)-2}{3^8+1}=\frac{3.\left(3^8+1\right)}{3^8+1}-\frac{2}{3^8+1}=3-\frac{2}{3^8+1}\)

mà \(\frac{2}{3^9+1}< \frac{2}{3^8+1}\Rightarrow3-\frac{2}{3^9+1}< 3-\frac{2}{3^8+1}\)

=> A < B

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