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

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

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

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

\(=49.50.51.52\)

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

Ta có : 1-2+3-4+5-6+7-...-48+49-50

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

=(-1)+(-1)+(-1)+...+(-1)

=(-1)*25

=-25

1-2+3-4+5-6+7-....-48+49-50

=(1-2)+(3-4)+(5-6)+(7-8)+.....+(47-48)+(49-50)     có 25 cặp số như thế

= -1   +  -1   +  -1   +  -1  +.....+    -1    +    -1

= -1 x 25

= -25

$A=\frac{1}{1.2}+$ $\frac{1}{2.3}+$ $\frac{1}{3.4}+...+$ $\frac{1}{49.50}$

⇒$A=1-\frac{1}{2}+$ $\frac{1}{2}-$ $\frac{1}{3}+...+$ $\frac{1}{49}-$ $\frac{1}{50}$ $A=1-\frac{1}{50}$

⇒$A=$$\frac{49}{}$

\(\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{49.50}\)

\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}\)

\(=\dfrac{1}{2}-\dfrac{1}{50}=\dfrac{12}{25}\)

ai đó giúp mik vs :((

a,1-2+3-4+...+49-50.

=(-1)+(-1)+...+(-1)

=-25

b,1-4+7-10+...-100+103

=(-3)+(-3)+...+(-3)+103

=(-150)+103

=-47

a) 1 - 2 + 3 - 4 + ... + 49 - 50

= -1 + (-1) + ... + (-1)

= -1 . [(50 - 1) + 1] : 2

= -1 . 25

= -25

b) 1 - 4 + 7 - 10 + ... - 100 + 103

= -3 + (-3) + ... + (-3) + 103

= -3 . [(100 - 1) : 3 + 1] : 2 + 103

= -3 . 34 : 2 + 103

= -3 . 17 + 103

= -51 + 103

= 52

Ta có 50 + 48 + 46 + ... + 4 + 2 - 1 - 3- 5 - ... -47 -49

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

=1+1+1+...+1+1

VÌ  từ 2 đến 50 có (50-2):2+1=25 ( số)

\(\Rightarrow\)có 25 số 1 cộng lại

\(\Rightarrow\)50+48+46+...+4+2-1-3-5-...-47-49 = 1\(\times\)25 =25

calculator

\(=49\times\left(55+48-3\right)=49\times100=4900\)

= 49 x (55 + 48 - 3)

= 49 x 100

= 4900

A=(198-1)(1998+1)=1998^2-1<B

M=2003^9.(2003+1)=2003^9.2004<N

P=2^50-1<Q

a) 5 . 125 . 2 . 41 . 8

= (5 . 8) . (125 . 2) . 41

= 40 . 250 . 41

= 10 000 . 41

= 410 000

b) 25 . 7 . 10 . 4

= (25 . 4 ) . (10 . 7)

= 100 . 70

= 7000

Chúc bạn học tốt!! ^^

a,5.125.2.41.8=(125.8).(2.5).41=1000.10.41=410000

b,25.7.10.4=(25.4).70=100.70=7000

c,8.12.125.2=(8.125).12.2=100.24=2400

d,4.36.25.50=(4.25).(2.50).18=100.100.18=180000

a) \(227+50+23=\left(227+23\right)+50=250+50=300\)

b) \(135+360+65+40=\left(135+65\right)+\left(360+40\right)=200+400=600\)

c) \(1+2+3+4+5+...+97+98+99+100\)

\(=\left(100+1\right)+\left(99+2\right)+...+\left(50+51\right)\)

\(=101+101+101+...+101\)

\(=101\cdot50\)

\(\Leftrightarrow5050\)

d) \(115\cdot13-13\cdot15=13\cdot\left(115-15\right)=13\cdot100=1300\)

e) \(50-49+48-47+...+4-3+2-1\)

\(=\left(50-49\right)+\left(48-47\right)+...+\left(2-1\right)\)

\(=1+1+1+1+..+1\)

\(=1\cdot25\)

\(=25\)

f) \(30\cdot40\cdot50\cdot60=10\cdot3+10\cdot4+10\cdot5+10\cdot6\)

\(=10\cdot10\cdot10\cdot10\cdot3\cdot4\cdot5\cdot6\)

\(=10000\cdot360\)

\(=3600000\)

g) \(27\cdot36+27\cdot64=27\cdot\left(36+64\right)=27\cdot100=2700\)

h) \(5\cdot2^2-18:3=5\cdot4-18:3=20-6=14\)

i) \(13\cdot17-256:16+14:7-2021^0\)

\(=13\cdot17-4^4:4^2+2-1\)

\(=13\cdot17-16+2-1\)

\(=13\cdot17-17\)

\(=17\cdot\left(13-1\right)\)

\(=204\)

j) \(7^2-36:3=49-12=37\)