Em ơi,chứng minh A gì nữa em????

\(A=\dfrac{1}{2^2}+\dfrac{1}{2^3}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{50^2}\)

\(A=\dfrac{1}{2\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot3}+\dfrac{1}{4\cdot4}+...+\dfrac{1}{50\cdot50}\)

\(A=\dfrac{1}{2}-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{3}+\dfrac{1}{4}-\dfrac{1}{4}+...+\dfrac{1}{50}-\dfrac{1}{50}\)

\(A=1\)

Vậy A=1

\(A=\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{50^2}\)

\(A=1+\left(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{50^2}\right)=1+B\)( Gọi biểu thức trong ngoặc là B)

Ta xét B

B=\(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{50^2}\)

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

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

B<\(1-\frac{1}{50}<1\)

Vậy B<1

=>A=1+B < 1+1=2

Vậy A<2

đặt B=1/1.2+1/2.3+...+1/49.50

ta có:

A=1/1^2+1/2^2+1/3^2+1/4^2+....+1/50^2<B=1/1.2+1/2.3+...+1/49.50 (1)

B=1/1.2+1/2.3+...+1/49.50

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

=1-1/50<1 (2)

từ (1) va (2)=>A<B<2

=>A<2

dễ lắm bn ạ  nhưng mk ko bt lm hhh

Ta có: A = 1/1 + 1/2 + ... + 1/50

2A = 2 + 1 + ... +1/25

2A - A = (2 + 1 + ... +1/25) - (1 + 1/2 + ... + 1/50)

A = 2 - 1/50

Vì 1/50 > 0 nên 2 - 1/50 < 2

Vậy A < 2 (đpcm)