Question

Tìm x biết

( x+1) + (x+2) + (x+3) + .... + (x+100) = 5750

Answer 1

\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+.........+\left(x+100\right)=5750\\ 100x+5050=5750\\ 100x=700\\ x=7\)

Answer 2

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

\(\Rightarrow\left(x+x+...+x\right)\left(1+2+3+...+99+100\right)=5750\)

\(\Rightarrow100x+5050=5750\)

\(\Rightarrow100x=5750-5050\)

\(\Rightarrow100x=200\)

\(\Rightarrow x=\frac{200}{100}\)

\(\Rightarrow x=2\)

Answer 3

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

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

\(\Leftrightarrow100x=5750-\frac{\left(1+100\right)\cdot100}{2}=5750-5050=700\)

\(\Leftrightarrow x=7\)

Answer 4

( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ... + ( x + 100 ) = 5750

( x + x + x + ... + x ) + ( 1 + 2 + 3 + ... + 100 ) = 5750

100 . x + 5050 = 5750

100 . x = 5750 - 5050

100 . x = 700

=> x = 700 : 100

=> x =  7

Vậy x = 7

Answer 5

ớ nhầm. sorry

Answer 6

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

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

\(100x+1+2+3+.....+100=5750\)
Từ 1 đến 100 có số các số hạng là: (100-1):1+1=100(số hạng)

\(100x+100.(100+1):2=5750\)

\(100x+5050=5750\)

\(100x=700\)

\(x=7\)

Answer 7

(x+1) + (x+2) + (x+3) + ......+ (x+100) = 5750

⇒(x+x+x+...+x) + (1+2+3+.....+100) = 5750

Có số số thừa số x là:

(100-1) : 1+1 = 100

Tổng của dãy 1+2+3+...+100 là:

(100+1) . 100 :2 = 5050

⇒100x + 5050 = 5750

⇒100x= 5750-5050

⇒100x= 700

⇒x=700:100

⇒x=7