Question

[Nguyễn Thị Giang]

Tính nhanh

A=2/1*5+2/5*9+2/9*13+...+2/97*101+2/101*105

B=4/2*5+4/5*2+4/8*11+...+4/44*47+4/47*50

C=3/1*3*5+3/3*5*7+3/5*7*9+...+3/19*21*23+3/21*23*25

Answer 1

[Lê Nguyên Bách]

A = 2/1*5 + 2/5*9 + ... + 2/101*105

   = 1/2(4/1*5 + 4/5*9 + ... + 4/101*105)

   = 1/2(1 - 1/5 + 1/5 - 1/9 + ... + 1/101 - 1/105)

   = 1/2(1 - 1/105)

   = 1/2 * 104/105 = 52/105

Sửa câu b. Phân số thứ 2 phải là 4/5*8

B = 4/2*5 + 4/5*8 + ... + 4/47*50

   = 4/3(3/2*5 + 3/5*8 + ... + 3/47*50)

   = 4/3(1/2 - 1/5 + 1/5 - 1/8 + ... + 1/47 - 1/50)

   = 4/3(1/2 - 1/50)

   = 4/3 * 24/50 = 16/25