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