Question

Tìm x biết (1/2+1/4+1/8+1/16):x=1/2+1/6+1/12+1/20+...+1/132

Answer 1

Ta có:

(1/2 + 1/4 + 1/8 + 1/16) = 8/16 + 4/16 + 2/16 + 1/16 = 15/16.

1/2 + 1/6 + 1/12 + 1/20 +…+ 1/132 = 1/(1.2) + 1/(2.3) + 1/(3.4) + 1/(4.5) +…+1/(11.12)

= (1 – 1/2) + (1/2 – 1/3) + (1/3 – 1/4) + (1/4 – 1/5) +…+ (1/11 – 1/12)

= 1 – 1/12 = 11/12

Vậy x = (15/16) : (11/12) = 45/44.

Answer 2

(1/2+1/4+1/8+1/16):x=1/2+1/6+1/12+1/20+...+1/132

(1-1/2+1/2-1/4+1/4-1/8+1/8-1/16):x=1/1x2+1/2x3+1/3x4+1/4x5+...+1/11x12

(1-1/16):x=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/11-1/12

15/16:x=1-1/12

15/16:x=11/12

x=15/16:11/12

x=45/44

Answer 3

45/44