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

=1-1/50<1

M=1/1.2+1/2.3+...+1/49.50

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

M=1-1/50<1

=>M<1

\(M=\frac{1}{1.2}+\frac{1}{2.3}+.....+\frac{1}{49.50}\)

\(M=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}\)

\(M=1-\frac{1}{50}<1\)

\(=>M<1\)

\(M=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}\)

\(M=1+\left(-\frac{1}{2}+\frac{1}{2}\right)+\left(-\frac{1}{3}+\frac{1}{3}\right)+...+\left(-\frac{1}{49}+\frac{1}{49}\right)-\frac{1}{50}\)

\(M=1+0+0+...+0-\frac{1}{50}\)

\(M=\frac{49}{50}\)

\(\Rightarrow\frac{49}{50}< 1\)

\(\Rightarrow M< 1\)

dấu chấm ở giữa hai số là dấu nhân à?

\(M=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{49\cdot50}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...+\frac{1}{49}-\frac{1}{50}\)

\(=1-\frac{1}{50}=\frac{49}{50}\)

Vì \(\frac{49}{50}< 1\)\(\Rightarrow M< 1\)

VẬY M < 1

HK TỐT #

\(M=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}\)

\(=1-\frac{1}{50}< 1\)

\(\Leftrightarrow M< 1\)

M\(=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}\)

\(=1-\frac{1}{50}

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+......+\frac{1}{49}-\frac{1}{50}\)

\(1-\frac{1}{50}=\frac{49}{50}\)

vì \(\frac{49}{50}

hình như ko phải so sánh mà là còn cái nịt (:

M =1/1.2+1/2.3+....+1/49.50

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

M=1/1-1/50

M=49/50

tính nha :-)

\(M=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}\)

     \(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}\)

      \(=1-\frac{1}{50}< 1\)

Vậy  \(M< 1\)

Sai đề rồi! Đề đúng là : So sánh :

1/1.2 + 1/2.3 +......+ 1//49.50 và 1

Bài làm : Gọi tổng trên là A

A = 1/1.2 + 1/2.3 +.......+ 1/49.50

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

A = 1 - 1/50

A = 49/50

Vì 49/50 < 1 => A < 1 nha!

Ai k mk mk k lại !

1/1.2+1/2.3+...+1/49.50 

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

(1-1/50)+(1/2-1/2)+.....+(1/49-1/49)

50/50-1/50+0+....+0

49/50

vì 49/50 < 1

=>  1/1.2+1/2.3+...+1/49.50 <1

đặt A=1/1.2+1/2.3+1/3.4+..........1/49.50

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}\)

\(A=1-\frac{1}{50}<1\)

vậy A<1

1/1.2 + 1/2.3 + 1/3.4 + ... + 1/49.50

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

1 - 1/50 < 1

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)

=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)

=\(1-\frac{1}{50}\)

Vì \(1-\frac{1}{50}\)< 1

Nên \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)< 1

=> đpcm

\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}\)(các phân số đối nhau tự động loại bỏ)

                                              \(=1-\frac{1}{50}