Question

Chứng tỏ rằng: 1/1.2+1/2.3+...+1/49.50=1/26+1/27+...+1/50

Answer 1

1/1.2+1/3.4+1/5.6+...+1/49.50=1/26+1/27+...+1/50

=1/1-1/2+1/3-1/4+...+1/49-1/50

=(1/1+1/3+...+1/49)-(1/2+1/4+...+1/50)

=(1/1+1/2+1/3+...+1/49+1/50)-2(1/2+1/4+...+1/50)

=1/1+1/2+1/3+...+1/50-1-1/2-1/3-...-1/25

=1/26+1/27+...+1/50 (đpcm)

Answer 2

1/1.2+1/3.4+1/5.6+...+1/49.50=1/26+1/27+...+1/50

=1/1-1/2+1/3-1/4+...+1/49-1/50

=(1/1+1/3+...+1/49)-(1/2+1/4+...+1/50)

=(1/1+1/2+1/3+...+1/49+1/50)-2(1/2+1/4+...+1/50)

=1/1+1/2+1/3+...+1/50-1-1/2-1/3-...-1/25

=1/26+1/27+...+1/50 (đpcm)

Answer 3

Hình như sai đề rồi bạn ạ

Answer 4

1/1.2+1/3.4+1/5.6+...+1/49.50=1/26+1/27+...+1/50

=1/1-1/2+1/3-1/4+...+1/49-1/50

=(1/1+1/3+...+1/49)-(1/2+1/4+...+1/50)

=(1/1+1/2+1/3+...+1/49+1/50)-2(1/2+1/4+...+1/50)

=1/1+1/2+1/3+...+1/50-1-1/2-1/3-...-1/25

=1/26+1/27+...+1/50 

=> đpcm

Cre: http://olm.vn/hoi-dap/question/79077.html?auto=1

Answer 5

1/1.2 + 1/3.4 + 1/5.6 + ... + 1/49.50 = 1/26 + 1/27 + ... + 1/50

= 1/1 - 1/2 + 1/3 - 1/4 + ... + 1/49 - 1/50

= (1/1 + 1/3 + ... + 1/49) - (1/2 + 1/4 + ... + 1/50)

= (1/1 + 1/2 + 1/3 + ... + 1/49 + 1/50) - 2(1/2 + 1/4 + ... + 1/50)

= 1/1 + 1/2 + 1/3 + ... + 1/50 - 1 - 1/2 - 1/3 - ... - 1/25

= 1/26 + 1/27 + ... + 1/50 

=> điều cần chứng minh