Question

[tran phuong]

tính A/B biết

A=\(1^2+2^2+...+300^2\)

B=\(175.43.601\)

ai làm xong trước  mình tick đúng cho

Answer 1

[Hiền Thương]

A = 1² + 2² + 3² + 4² +...+300²

A = 1.1 + 2.2 + 3.3 + 4.4 + ...+300.300

A= 1.(2-1) + 2.(3-1) + 3.(4-1) +  4.(5-1) +....+300.(301-1) 

A = 1.2 + 2.3 + 3.4 + 4.5 + ....+ 300.301 - (1+2+3+...+300)

Đặt E = 1.2+2.3 +.3.4 + 4.5 + ...+300.301 

=> 3E = 1.2.3 + 2.3.3+3.4.3 + 4.5.3 +....+300.301.3

3E = 1.2.3+2.3.(4-1)+3.4.(5-2)+4.5.(6-3)+...+300.301.(302-299)

3E= 1.2.3+2.3.4-2.3.1+3.4.5-3.4.2+4.5.6-4.5.3+...+300.301.302-300.301.299

3E= 300.301.302

E=\(\frac{300\cdot301\cdot302}{3}\)

E = 9 090 200

=> A = 9 090 200 - (1+2+..+300)

=> A = 9 090 200 - \(\frac{300\cdot301}{2}\)

=> A = 9 090 200 - 45 150 

=> A = 9 045 050

mà B = 175 . 43 . 601 = 4 522 525 

=> \(\frac{A}{B}=\frac{9045050}{4522525}=2\)

vậy A/B =2