\(S=\left(1-\dfrac{1}{2^2}\right)\left(1-\dfrac{1}{3^2}\right)\left(1-\dfrac{1}{4^2}\right)\left(1-\dfrac{1}{5^2}\right)...\left(1-\dfrac{1}{99^2}\right)\)
\(=\left(1-\dfrac{1}{2}\right)\left(1+\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1+\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)\left(1+\dfrac{1}{4}\right)...\left(1-\dfrac{1}{99}\right)\left(1+\dfrac{1}{99}\right)\)
\(=\dfrac{1}{2}\cdot\dfrac{3}{2}\cdot\dfrac{2}{3}\cdot\dfrac{4}{3}\cdot\dfrac{3}{4}\cdot...\cdot\dfrac{98}{99}\cdot\dfrac{100}{99}\)
\(=\dfrac{1}{2}\cdot\dfrac{100}{99}\)
\(=\dfrac{50}{99}\)
Đúng 1
Bình luận (0)
