Question

(x+1)+(x+2)+(x+3)+...+(x+100)=5150

 

Answer 1

\((x+1)+(x+2)+(x+3)+(x+4)+...+(x+100) = 5150 100* x + (1 + 2 + 3 + 4 + ... + 100) = 5150 100* x + 5050 = 5150 100 * x = 100 x = 100 : 100 x = 1 \)

Answer 2

(x+1)+(x+2)+(x+3)+(x+4)+...+(x+100) = 5150 
100* x + (1 + 2 + 3 + 4 + ... + 100) = 5150 
100* x + 5050 = 5150 
100 * x = 100 
x = 100 : 100 
x = 1 

Answer 3

x=1nha 
ta co:1+2+3+4+5+...+n 
=n.(n+1)/2 
nen 1+2+3+4+...+100 
=100.101/2=5050 
pt ban dau <=>100x+5050=5150 
<=>100x=100 
<=>x=1

Answer 4

(x+1)+(x+2)+(x+3)+...+(x+100)=5150

(x+x+x+...+x)+(1+2+3+...+100)=5150

100.x+(1+2+3+...+100)=5150

Ta xét :

A=1+2+3+...+100

A=100+99+98+...+1

⇒A+A=(1+100)+(2+99)+(3+98)+...+(100+1)

2A=101+101+101+...+101(có 100 số101)

2A=101 . 100

A= 101 . 100 :2

A= 10100:2

A= 5050

⇒ 100.x+(1+2+3+...+100)=5150

100.x + 5050 = 5150

100.x = 5150-5050

100.x=100

x=100:100

x=1

Vậy x = 1