1942/2907

nhanh lên nhé

=\(55^{6x11}và66^{5x11}\)

=\(330^{11}va330^{11}\)

=>\(55^{66}=66^{55}\)

Vì tập hợp A gồm các số chia hết cho cả 3 và 5 mà 3 và 5 nguyên tố cùng nhau 

=> BCNN( 3 , 5 ) = 3 . 5 = 15

=> BC( 3 , 5 ) = { 0 ; 15 ; 30 ; 45 ; ... }

=> A = { 0 ; 15 ; 30 ; 45 ; ... } mà các phần tử của tập hợp A bao gồm các số tự nhiên lẻ nhỏ hơn 100

=> A = { 0 ; 15 ; 45 ; 75 } ( có 4 phần tử )

chỉ có ba phần tử là 15 ,45 , 75

\(\frac{1}{2}.\frac{2}{3}=\frac{1}{3}\)

\(\frac{66}{5}:\frac{3}{5}=\frac{66}{5}.\frac{5}{3}=22\)

\(\frac{1}{2}\cdot\frac{2}{3}=\frac{1.2}{2.3}=\frac{1.1}{1.3}=\frac{1}{3}\)

\(\frac{66}{5}:\frac{3}{5}=\frac{66}{5}\cdot\frac{5}{3}=\frac{66.5}{5.3}=\frac{22.1}{1.1}=22\)

Ta có : 55⁶⁶ = [(11.5)⁶]¹¹ = (11⁶ . 5⁶)¹¹ = (11⁵ . 11 . 5⁶)¹¹

66⁵⁵ = [(11.6)⁵]¹¹ = (11⁵ . 6⁵)¹¹

Vì 11 . 5⁶ > 6⁵ nên 55⁶⁶ > 66⁵⁵

\(55^{66}=\left(55^6\right)^{11}=\left[\left(11.5\right)^6\right]^{11}=\left(11^6.5^6\right)^{11}=\left(11^5.11.5^6\right)^{11}\)

\(66^{55}=\left(66^5\right)^{11}=\left[\left(11.6\right)^5\right]^{11}=\left(11^5.6^5\right)^{11}\)

Vì : \(11.5^6>6^5\)

Vậy : \(55^{66}>66^{55}\)

Ta có : 55⁶⁶ = [(11.5)⁶]¹¹ = (11⁶ . 5⁶)¹¹ = (11⁵ . 11 . 5⁶)¹¹

66⁵⁵ = [(11.6)⁵]¹¹ = (11⁵ . 6⁵)¹¹

Vì 11 . 5⁶ > 6⁵ nên 55⁶⁶ > 66⁵⁵

\(\frac{1}{6}+\frac{1}{66}+\frac{1}{176}+\frac{1}{336}+...+\frac{1}{1886}\)

\(=\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+\frac{1}{16.21}+...+\frac{1}{41.46}\)

\(=\frac{5}{5}\left(\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+\frac{1}{16.21}+...+\frac{1}{41.46}\right)\)

\(=\frac{1}{5}\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{41.46}\right)\)

\(=\frac{1}{5}\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{41}-\frac{1}{46}\right)\)

\(=\frac{1}{5}\left(1-\frac{1}{46}\right)\)

\(=\frac{1}{5}.\frac{45}{46}=\frac{9}{46}\)

1/(1.6) + 1/(6.11) + 1/(11.16) + … + 1/[(5n-4)(5n+1)] 
=(1/1 – 1/6)/5 + (1/6 – 1/11)/5 + (1/11 – 1/16)/5 +…+ [1/(5n-4) – 1/(5n+1)]/5 
=[1/1 – 1/6 + 1/6 – 1/11 + 1/11 – 1/16 + … + 1/(5n-4) – 1/(5n+1)]/5 
=[1 – 1/(5n+1)]/5 

=[1 – 1/(5.100+1)]/5 = 100/501

\(-66\cdot\left[\frac{1}{2}-\frac{1}{3}+\frac{1}{11}\right]+124\cdot\left[-37\right]+63\cdot\left[-1+24\right]\)

\(=-66\cdot\left[\frac{1}{6}+\frac{1}{11}\right]+\left[-4588\right]+63\cdot23\)

\(=-66\cdot\frac{17}{66}+\left[-4588\right]+1449\)

\(=-17+\left[-4588\right]+1449=-4605+1449=-3156\)

Các bạn ủng hộ cho mình nhé

\(5B=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{496.501}\)

\(5B=\frac{6-1}{1.6}+\frac{11-6}{6.11}+\frac{16-11}{11.16}+\frac{21-16}{16.21}+...+\frac{501-496}{496.501}\)

\(5B=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{496}-\frac{1}{501}\)

\(5B=1-\frac{1}{501}=\frac{500}{501}\Rightarrow B=\frac{100}{501}\)

1A  = 1/6 . (1 - 1/501) = 1/6 . 500/501 => A = 500/501.6=500/3006

=1/1*6+1/6*11+1/11*16+1/16*31+...+1/496+1/496*501

=1/5*(1-1/6*1/6-1/11+1/11-1/16+1/16-1/31+...+1/496-1/501)

=1/5*(1-1/501)

=1/5*500/501

=100/101

Vậy A=100/101