Question

[Why Not Me]

\(A=\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{50^2}\) Chứng tỏ  rằng A < 2

Answer 1

[zZz Phan Cả Phát zZz]

Ta có: 1/2² < 1/1.2

          1/3² < 1/2.3 

          1 /4 ² < 1/3.4

    .. .........................

        1/50² < 1/49.50
=> A < 1/1² + 1/1.2 + 1/2.3 + 1/3.4+......+1/49.50

=> A < 1 + (1-1/50)

=> A < 1+49/50

=> A < 99/55 <2

=> A < 2 

Answer 2

[l҉o҉n҉g҉ d҉z҉]

Ta có: 1/2² < 1/1.2

          1/3² < 1/2.3 

          1 /4 ² < 1/3.4

    .. .........................

        1/50² < 1/49.50
=> A < 1/1² + 1/1.2 + 1/2.3 + 1/3.4+......+1/49.50

=> A < 1 + (1-1/50)

=> A < 1+49/50

=> A < 99/55 <2

=> A < 2