Question

So sánh M= 1/ 1.2 + 1/ 2. 3 + ..........+ 1/ 49. 50 với 1

Answer 1

\(M=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)

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

\(\Rightarrow1>M\)

Answer 2

Ta có: 1/1.2+1/2.3+...+1/49.50

=        1-1/2+1/2-1/3+...+1/49-1/50

=        1-1/50

Ta có: 1-1/50 < 1 (luôn luôn đúng)

=> M<1

Answer 3

Ta có: 1/1.2+1/2.3+...+1/49.50

=        1-1/2+1/2-1/3+...+1/49-1/50

=        1-1/50

Ta có: 1-1/50 <  1 

=> M<1

 Tỉ ơi tích cho Đệ cái nha !!!

Answer 4

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

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

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

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

Vì \(\frac{49}{50}\) < 1 

\(\Rightarrow\)\(M<1\)

Answer 5

M=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

 M=1-1/50

SUY RA M<1

Answer 6

M=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

M=1-1/50

SUY RA M<1

Answer 7

M nhỏ hơn 1

Answer 8

Theo bài ra ta có : \(M=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}\)

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

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

Answer 9

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