Question

Tìm x thuộc N biết:

a)  x+ (x+1)+(x+2)+...+ (x+30) =1240

b)1+2+3+...+ x =210

Answer 1

a) \(x+\left(x+1\right)+......+\left(x+30\right)=1240\\ \Rightarrow31x+465=1240\\ \Rightarrow31x=775\\ \Rightarrow x=25\)

b) \(1+2+3+.........+x=210\\ \Rightarrow\frac{\left(x+1\right)x}{2}=210\\ \Rightarrow\left(x+1\right)x=420\\ \Rightarrow x=20\)

Answer 2

a)

x + (x + 1) + (x + 2) + ... + (x + 30) = 1240

x + x + 1 + x + 2 + ... + x + 30 = 1240

(x + x + ... + x) + (1 + 2 + ... + 30) = 1240

(x . [30 - 1 + 1 + 1]) + ([30 + 1] . [30 - 1 + 1] : 2) = 1240

31x + 465 = 1240

           31x = 1240 - 465

           31x = 775

                x = 775 : 31

                x = 25

b) 1 + 2 + 3 + ... + x = 210

(x + 1) . (x - 1 + 1) : 2 = 210

     (x + 1) . (x - 1 + 1) = 210 . 2

     (x + 1) . (x - 1 + 1) = 420

                   (x + 1) . x = 420

Mà 20 . 21 = 420 => x = 20

Answer 3

a)

x + (x + 1) + (x + 2) + ... + (x + 30) = 1240

x + x + 1 + x + 2 + ... + x + 30 = 1240

(x + x + ... + x) + (1 + 2 + ... + 30) = 1240

(x . [30 - 1 + 1 + 1]) + ([30 + 1] . [30 - 1 + 1] : 2) = 1240

31x + 465 = 1240

           31x = 1240 - 465

           31x = 775

                x = 775 : 31

                x = 25

b) 1 + 2 + 3 + ... + x = 210

(x + 1) . (x - 1 + 1) : 2 = 210

     (x + 1) . (x - 1 + 1) = 210 . 2

     (x + 1) . (x - 1 + 1) = 420

                   (x + 1) . x = 420

Mà 20 . 21 = 420 => x = 20