Question

tìm x biết (x + 1) + (x + 2) + (x + 3) + (x + 4 + ... + (x + 99) + (x + 100) = 102x

Answer 1

100x+5050=102x

100x+5050=100x+2x

=>2x=5050

x=5050/2

x=2525

Answer 2

(x + 1) + (x + 2) + ... + (x + 100) = 102x

x + x + x + ... + x + 1 + 2 + ... + 100 = 102x

100x + (100 + 1) x 100 : 2 = 102x

102x - 100x = 5050

2x = 5050

x = 2525

Answer 3

(x + 1) + (x + 2) + (x + 3) + (x + 4 ) + ... + (x + 99) + (x + 100) = 102x

(x+x+x+...+x)+(1+2+3+4+...+100) = 102x

100x + 5050 = 102x

<=>102x-100x=5050

(102-100)x=5050

2x=5050

x=5050:2

x=2525

Answer 4

(x+1) + (x+2) + (x+3) + (x+4) +...+ (x+99) + (x+100) =102x

số số hạng của tổng 100-1+1=100

x + 1 + x + 2 + x + 3 + x + 4 +... + x + 99 + x + 100 = 102x

100x + (1 + 2 + 3 + 4  +...+ 99 + 100) = 102x

ta có 1 + 2 + 3 + 4  +...+ 99 + 100

       =(100 + 1).100 : 2

       =(100 + 1).50

       =5050

nên 100x + (1 + 2 + 3 + 4  +...+ 99 + 100) = 102x

<=> 100x + 5050 = 102x

<=> 5050 = 102x - 100x

<=>5050 = 2x

<=>x = 5050 : 2 = 2525

vậy x = 2525