(x+2)+(x+4)+...+(x+1996) = 99800

=> (x+x+x+...+x)+(2+4+...+1996) = 99800

=> 998x + 997002 = 99800

998x = 99800 - 997002

998x = -897202

x = -897202 : 998

x = -899

\(c,\)\(\left(x-1\right)+\left(x-2\right)+....+\left(x-100\right)=50\)

\(\left(x+x+...+x\right)-\left(1+2+...+100\right)=50\)

\(100x-5050=50\)

\(100x=50+5050\)

\(100x=5100\)

\(\Rightarrow x=\frac{5100}{100}=51\)

\(a,\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+....+\left(x+100\right)=5750\)

\(\left(x+x+x+...+x\right)+\left(1+2+3+...+100\right)=5750\)

\(100x+5050=5750\)

\(100x=5750-5050\)

\(100x=700\)

\(\Rightarrow x=7\)

\(b,x+\left(1+2+3+...+50\right)=2000\)

 \(x+\frac{\left[1+50\right]\cdot\left[\left(50-1\right)\div1+1\right]}{2}=2000\)

\(x+1275=2000\)

\(\Rightarrow x=2000-1275=725\)

c , ( x - 1 ) + ( x - 2 ) + ...... + ( x - 100 ) = 50

( x + x + ........ + ) - ( 1 + 2 + ..... + 100 ) = 50

100x - 5050 = 50

100x = 50 + 5050

100x = 5100

=> x = 5100/100 = 51

=49x50x51

=124950

trên mạng có CM 1 x 2 + 2 x 3 + 3 x 4+ 4 x 5 + ... + n x (n+1) = n x (n+1) x (n+2)

lấy máy tính mà tính

\(\frac{49\cdot50\cdot51}{3}\)

4 × 125 × 25 × 8

= (4 × 25) × (125 × 8)

= 100 × 1000

= 100 000

2 × 8 × 50 × 25 × 125

= (2 × 50) × (8 × 125) × 25

= 100 × 1000 × 125

= 12 500 000

2 × 3 × 4 × 5 × 50 × 25

= (2 × 50) × (4 × 25) × (3 × 5)

= 100 × 100 × 15

= 150 000

25 × 20 × 125 × 8 - 8 × 20 × 5 × 125

= 8 × 125 × 20 × (25 - 5)

= 1000 × 20 × 20

= 400 000

- (25 x 4) x (125 x8)=100 x 1000 =100000

- (50 x 2) x (8 x 125) x 25=100 x 1000 x 25 =2500000

- (2 x 50 ) x (4 x 25) x (3 x5)=100 x 100 x 15=150000

- 25 x 20 x125 x 8 - 5

= (20 x 5) x (125 x 8) -25=100 x 1000 -5 =100000 - 5 =99995

4 *125*25*8

=4*25*125*8

=100*1000

=100000

2*8*50*25*125

=2*50*8*125*25

=100*1000*25

=2500000

2*3*4*5*50*25

=2*50*4*25*3*5

=100*100*15

=150000

25*20*125*8-8*20*5*125

=25*4*5*125*8-8*125*20*5

=100*1000*5-1000*100

=500000-100000

=400000

=

X + 2 x X + 3 x X + 4 x X = 50

X x ( 1+2+3+4) =50

X x 10 =50

X =50 : 10

X =5

X + 2 x X + 3 x X+ 4 x X = 50 

X x (1+ 2 + 3 + 4 )    = 50 

X x 10 = 50 

X = 50 : 10 

X = 5