Question

ChoA=1/1^2+1/2^2+1/3^2+1/4^2+...+1/50^2

Chung minh A <2

Answer 1

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

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

\(=1-\frac{1}{50}< 1< 2\Rightarrow A< 2\Rightarrowđpcm\)

Answer 2

thanks ban vi minh dang rat can dap an nay

Answer 3

\(A=\frac{1}{1^2}+\frac{1}{2^2}+.....+\frac{1}{50^2}\)

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

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

\(=2-\frac{1}{50}< 2\)

Vậy A<2

Answer 4

Theo cách của bạn không cần biết thì A> chứ