Question

Tìm x biết

(\(\dfrac{2}{1.3}\)+\(\dfrac{2}{3.5}\)+\(\dfrac{2}{5.7}\)+...+\(\dfrac{2}{97.99}\)) - x =\(\dfrac{-100}{99}\)

Answer 1

x= -2

-Lớp lớn rồi nên không biết làm bài này, chỉ dùng máy tính tính thôi-

Answer 2

\(\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{97.99}\right)-x=-\dfrac{100}{99}\)

\(\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{99}\right)-x=-\dfrac{100}{99}\)

\(\left(1-\dfrac{1}{99}\right)-x=-\dfrac{100}{99}\)

\(\dfrac{98}{99}-x=-\dfrac{100}{99}\)

\(x=\dfrac{98}{99}-\left(-\dfrac{100}{99}\right)\)

\(x=\dfrac{198}{99}\)

Vậy \(x=\dfrac{198}{99}\)