\(B=1^2+2\left(1+1\right)+3\left(2+1\right)+4\left(3+1\right)+100\left(99+1\right)=\)

\(=\left(1+2+3+...+100\right)+\left(1.2+2.3+3.4+...+99.100\right)=\)

1+2+3+...+100 tổng cấp số cộng d=1

\(1.2+2.3+3.4+...+99.100=\)

\(=\dfrac{1}{3}\left(1.2.3+2.3.3+3.4.3+...+99.100.3\right)=\)

\(=\dfrac{1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+99.100.\left(101-98\right)}{3}=\)

\(=\dfrac{1.2.3-1.2.3+2.3.4-2.3.4+3.4.5-.....-98.99.100+99.100.101}{3}=\)

\(=\dfrac{99.100.101}{3}=33.100.101\)

Thay các kết quả vào để tính B

\(x=0-\dfrac{1}{2}\)

\(x=-\dfrac{1}{2}\)

x+1/2 = 0

= x = 0-1/2

= x = -1/2

Ta có: \(n+2⋮n-1\)

\(\Leftrightarrow n-1+3⋮n-1\)

\(\Leftrightarrow3⋮n-1\)

Vì \(n\in Z\)\(\Rightarrow n-1\inƯ\left(3\right)=\left\{\pm1;\pm3\right\}\)

\(\Leftrightarrow n\in\left\{2;0;4;-2\right\}\)

Vậy....

\(n+2⋮n-1\)

<=> (n-1) +3 \(⋮\) n-1

Vì n-1\(⋮\) n-1 

Để n+2\(⋮\) n-1 => 3\(⋮\) n-1 hay n-1\(\inƯ\left(3\right)=\left\{1;3;-1;-3\right\}\)

=> n \(\in\left\{2;4;0;-2\right\}\)

Giúp mình vs ạ 

Bài 1:

a.\(150+50:5-2.3^2\)

\(=150+50:5-2.9\)

\(=150+10-18\)

\(=160-18\)

\(=142\)

b,\(375+693+625+307\)

\(=375+625+\left(693+307\right)\)

\(=1000+1000\)

\(=2000\)

e.\(500-\left\{5\left[409-\left(2^3.3-21\right)^2\right]-1724\right\}\)

\(=500-\left\{5\left[409-\left(8.3-21\right)^2\right]-1724\right\}\)

\(=500-\left\{5\left[409-\left(24-21\right)^2\right]-1724\right\}\)

\(=500-\left\{5\left[409-3^2\right]-1724\right\}\)

\(=500-\left\{5\left[409-9\right]-1724\right\}\)

\(=500-\left\{5.400-1724\right\}\)

\(=500-\left\{2000-1724\right\}\)

\(=500-276\)

\(=224\)

d.\(2^4.5-\left[131-\left(13-4\right)^2\right]\)

\(=16.5-\left[131-11^2\right]\)

\(=80-\left[131-121\right]\)

\(=80-10\)

\(=60\)

c.\(4.2^3-3^4:3^3+25^2:5^2\)

\(=4.8-3^1+625:25\)

\(=32-3+25\)

\(=29+25\)

\(=54\)

Bài 2:

a.\(219-7\left(x+1\right)=100\)

\(7\left(x+1\right)=219-100\)

\(7\left(x+1\right)=119\)

\(x+1=119:7\)

\(x+1=17\)

\(x=17-1\)

\(x=16\)

b.(3x-6)3=36

=>3x-6=36:3

=>3x-6=12

=>3x=12+6

=>3x=18

=>x=18:3

=>x=6

c.716-(x-143)=659

=>x-143=716-659

=>x-143=57

=>x=57+143

=>x=200

d.30-[4(x-2)+15]=3

=>4(x-2)+15=30-3

=>4(x-2)+15=27

=>4(x-2)=27-15

=>4(x-2)=12

=>x-2=12:4

=>x-2=3

=>x=3+2

=>x=5

e.\(\text{[(8x-12):4]3}^3=3^6\)

=>[(8x-12):4]27=729

=>(8x-12):4=729:27

=>(8x-12):4=27

=>8x-12=27.4

=>8x-12=108

=>8x=108+12

=>8x=120

=>x=120:8

=>x=15

hãy kết bạn với tui đi

gọi số tự nhiên càn tìm là a
Ta có:  a:12 dư 5      a-5 chia hết cho 12
            a:18 dư 5 =>a-5 chia hết cho 18
            a:21 dư 5      a-5 chia hết cho21
    => a-5 thuộc BC(12,18,21)
  12=2^2 . 3      =>BCNN(12,18,21)=2^2 .3^2 .7=252
   18=2 . 3^2   =>BC(12,18,21)=B(252)=
   21=3 . 7                                                  

   =>BC(12,18,21)=B(252)=B(252)=(...-1008;-756,-504;-252;0;252;504;756,1008,...)

  Mà a nhỏ hơn 1000 và lớn hơn 700 => a =756

Vậy a=756