Question

So sánh:

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

Khó hăm m.n !!!:))

Answer 1

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

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

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

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

Mà \(\frac{49}{50}\)lại nhỏ hơn 1 \(\Rightarrow\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}< 1\)

Answer 2

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

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

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

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

Answer 3

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

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

=1/1-1/50

=50/50-1/50=49/50 <1 

\(\Rightarrow\)1/1*2+1/2*3+...+1/49*50 < 1

\(\Rightarrow\)đpcm

Answer 4

=49/50 nha bạn

Answer 5

Ta có:

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

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

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

Vậy biểu thức trên bé hơn 1.