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18 tháng 10 2022

           B =     4 +  43 + 45 +.....+449

     42.B =            43 + 45+......+449 + 451

16B - B =    451 - 4

      15B =  ( 451-4)

         B = (451 - 4): 16

a: =-2/49-5/3+2/49=-5/3

b: \(=\dfrac{5\cdot4^{15}\cdot9^9-4\cdot3^{20}\cdot8^9}{5\cdot2^9\cdot6^{19}-7\cdot2^{29}\cdot27^6}\)

\(=\dfrac{5\cdot2^{30}\cdot3^{18}-3^{20}\cdot2^{27}\cdot2^2}{5\cdot2^9\cdot2^{19}\cdot3^{19}-7\cdot2^{29}\cdot3^{18}}\)

\(=\dfrac{5\cdot2^{30}\cdot3^{18}-3^{20}\cdot2^{29}}{5\cdot2^{28}\cdot3^{19}-7\cdot2^{29}\cdot3^{18}}\)

\(=\dfrac{2^{29}\cdot3^{18}\left(2\cdot3-3^2\right)}{2^{28}\cdot3^{18}\left(5\cdot3-7\cdot2\right)}=2\cdot\dfrac{6-9}{15-14}=2\cdot\left(-3\right)=-6\)

DT
27 tháng 1

\(B=4+4^3+4^5+...+4^{49}\\ \Rightarrow4^2.B=4^3+4^5+4^7+....+4^{51}\\ \Rightarrow16B-B=\left(4^3+4^5+4^7+...+4^{51}\right)-\left(4+4^3+4^5+...+4^{49}\right)\\ \Rightarrow15B=4^{51}-4\\ \Rightarrow B=\dfrac{4^{51}-4}{15}\)

25 tháng 4 2023

a\()\) 16/9 +3/5

=107/45

b\()\) 4/13--2/17

=51/221--26/221

=77/221

c\()\) -3/2+4/5

=-15/10+8/10

=-7/10

d\()\) 3/-4-1/4

=-1

e\()\) -1/5.5/7

=-1/7

f\()\) 7/8.64/49

=8/7

g\()\) 3/4.15/24

=15/32

 

28 tháng 12 2019

\(B=1.2.3+2.3.4+3.4.5+.......+49.50.51\)

\(\Rightarrow4B=1.2.3.4+2.3.4.4+3.4.5.4+.......+49.50.51.4\)

\(=1.2.3.4+2.3.4\left(5-1\right)+3.4.5\left(6-2\right)+.........+49.50.51.\left(52-48\right)\)

\(=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+.........+49.50.51.52-48.49.50.51\)

\(=49.50.51.52\)

\(\Rightarrow B=\frac{49.50.51.52}{4}=1624350\)

A = - ( 5 - 6 ) - ( 3 - 4 + 5 - 7 )

A = -5 + 6 - 3 + 4 - 5 + 7

A = ( 6 + 4 ) + ( -5 + (-5) ) + ( -3 + 7 )

A = 10 + (-10) + 4

A = 0 + 4

A = 4

P = ( 1 + 3 + 5 + ... + 47 + 49 ) - ( 2 + 4 + 6 + ... + 48 + 50 )

P = \(\frac{\left(1+49\right)\cdot\left(\left(49-1\right):2+1\right)}{2}\)  -  \(\frac{\left(2+50\right)\cdot\left(\left(50-2\right):2+1\right)}{2}\)

P = \(625-650\)

P = \(-25\)

NV
1 tháng 3 2023

\(\dfrac{5}{3\times4}+\dfrac{5}{4\times5}+...+\dfrac{5}{49\times50}\)

\(=5\times\left(\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+...+\dfrac{1}{49\times50}\right)\)

\(=5\times\left(\dfrac{4-3}{3\times4}+\dfrac{5-4}{4\times5}+...+\dfrac{50-49}{49\times50}\right)\)

\(=5\times\left(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{49}-\dfrac{1}{50}\right)\)

\(=5\times\left(\dfrac{1}{3}-\dfrac{1}{50}\right)=5\times\left(\dfrac{50}{150}-\dfrac{3}{150}\right)\)

\(=\dfrac{5\times47}{150}=\dfrac{47}{30}\)