Question

Cho:

A=1/1^2+1/2^2+...+1/50^2

Chứng minh A < 2.

Answer 1

Ta có: A < \(\frac{1}{1^2}+\frac{1}{1.2}+...+\frac{1}{49.50}\)

          A < \(1+\frac{1}{1.2}+...+\frac{1}{49.50}\)

          A < 1 + (1 - 1/50)

          A < 1 + 49/50

Vì 1 + 49/50 < 2 nên A < 1 + 49/50 < 2

Vậy A < 2 

nếu đúng thì cho mk biết nha

Answer 2

\(\frac{1}{1^2}=1\)

\(\frac{1}{2^2}<\frac{1}{1.2}\)

\(\frac{1}{3^2}<\frac{1}{2.3}\)

.....................

\(\frac{1}{50^2}<\frac{1}{49.50}\)

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

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

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

mà \(\frac{49}{50}<1=1<2\)

\(\Rightarrow A<2\)