tính nhanh

 1/2+1/10+1/50+1/250+1/1250

= 0,5 + 0,1 + 0,02 + 0,004 + 0,0008 

= 0,6248

tao chịu
 

a. 49 - 37 + 10 = 12 + 10 = 22

b. 57 . 49 + 57 . 51 - 120 = 57 . ( 49 + 51 ) -120 = 57 . 100 -120 = 5700 - 120 = 5580

c. 1250 - 11 . [ 37 . (2.3² -15)² ] =1250 - 11 .[ 37.  3² ] = 1250 - 11 . 333 = 1250 - 3663 = -2413

2x + 17 = 3 ³

2x + 17 = 27

2x         = 27 - 17

2x         =   10

x           =  10 : 2

x           =     5

4 . (x - 23 ) = 12

       x - 23  =  12 : 4

       x - 23  =      3

      x           =   23 - 3

      x          =    20

a)49-37+10

=49-(37+10)

=49-47

=2

b)57.49 +57. 51 -120

=57.(120+57).(51-49)

=57.(177.2)

=57.354

=20178

c)1250-11.[ 37 (2 . 3² -15)²

=1250-11.[37.(2.9-15)²

=1250-11.(37.3²)

=1250-11.(37.9)

=1509.333

=502497.

\(1,\sqrt{432}-\sqrt{363}+\sqrt{48}-\sqrt{75}+\sqrt{108}-\sqrt{147}\)

\(=\sqrt{12^2.3}-\sqrt{11^2.3}+\sqrt{4^2.3}-\sqrt{5^2.3}+\sqrt{6^2.3}-\sqrt{7^2.3}\)

\(=12\sqrt{3}-11\sqrt{3}+4\sqrt{3}-5\sqrt{3}+6\sqrt{3}-7\sqrt{3}\)

\(=\sqrt{3}.\left(12-11+4-5+6-7\right)\)

\(=-\sqrt{3}\)

\(2,6\sqrt{60}-5\sqrt{8}+3\sqrt{15}+4\sqrt{32}+3\sqrt{128}-2\sqrt{1250}\)

\(=6.2\sqrt{15}-5.2\sqrt{2}+3\sqrt{15}+4.4\sqrt{2}+3.8\sqrt{2}-2.25\sqrt{2}\)

\(=12\sqrt{15}+3\sqrt{15}-10\sqrt{2}+16\sqrt{2}+24\sqrt{2}-50\sqrt{2}\)

\(=\sqrt{15}.\left(12+3\right)+\sqrt{2}.\left(-10+16+24-50\right)\)

\(=15\sqrt{15}-20\sqrt{2}\)

1/ \(\sqrt{432}-\sqrt{363}+\sqrt{48}-\sqrt{75}+\sqrt{108}-\sqrt{147}\)

\(=12\sqrt{3}-11\sqrt{3}+4\sqrt{3}-5\sqrt{3}+6\sqrt{3}-7\sqrt{3}\)

\(=\left(12-11+4-5+6-7\right)\sqrt{3}\)

\(=-\sqrt{3}\)

2/ \(6\sqrt{60}-5\sqrt{8}+3\sqrt{15}+4\sqrt{32}+3\sqrt{128}-2\sqrt{1250}\)

\(=12\sqrt{15}-10\sqrt{2}+3\sqrt{15}+16\sqrt{2}+24\sqrt{2}-50\sqrt{2}\)

\(=\left(12+3\right)\sqrt{15}+\left(-10+16+24-50\right)\sqrt{2}\)

\(=15\sqrt{15}-20\sqrt{2}\)

A = 1 +  (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4)+...+ (1 + 2 + 3+...+ 30)

A = 1 + (2+1)\(\times\)2: 2+ (3+1)\(\times\)3: 2 + ....+ (30 +1) \(\times\) 30: 2 

A = 1 + 2 \(\times\)3: 2 + 3 \(\times\) 4 : 2 +...+ 30 \(\times\) 31:2

A = \(\dfrac{2+2\times3+3\times4+...+30\times31}{2}\)

Đặt B  = 2 + 2 \(\times\) 3 + 3 \(\times\) 4 +...+ 30 \(\times\) 31

   1 x 2 x 3 = 1 x 2 x3           = 1 x 2 x 3

   2 x 3 x 3 = 2 x 3 x ( 4 - 1) = 2 x 3 x 4 - 1 x 2 x 3

   3 x 4 x 3 = 3 x 4 x (5- 2)   = 3 x 4 x 5 - 2 x 3 x 4 

   ...........................................................................

   30 x 31 x 3 = 30 x 31 x (32 - 29) = 30 x 31 x 32 - 29 x 31 x 30

   Cộng vế với vế ta có: 

B x 3 = 30 x 31 x 32 ⇒ B = 30 x 31 x 32 : 3 = 14880

A = B : 2 = 14880 : 2 = 7440

=1/2 - 1/3 +1/3 - 1/4 +...+1/2016 - 1/2017
=1/2 - 1/2017
=...

1/2:3+1/3:4+1/4:5+...1/2016:2017

1/2.1/3+1/3.1/4+1/4.1/5+...1/2016.1/2017

1/2.3+1/3.4+1/4.5+...1/2016.2017

1/2-1/3+1/3-1/4+1/4-1/5+...1/2016-1/2017

=1/2-1/2017

=2017/4034-2/4034

=2015/4034

1/1*2+1/2*3+1/3*4+1/5*6

=1-1/2+1/2-1/3+1/3-1/4+1/5-1/6

=1-1/4+1/5-1/6

=47/60

\(\frac{1}{1}\cdot2+\frac{1}{2}\cdot3+\frac{1}{3}\cdot4+\frac{1}{5}\cdot6\)

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

\(=\frac{181}{30}\)