Question

\(\dfrac{4}{3.5}\) + \(\dfrac{8}{5.9}\) + \(\dfrac{12}{9.15}\)+.......+

\(\dfrac{32}{x(x+16)}\) = \(\dfrac{16}{15}\)

\(\dfrac{32}{x(x+16)}\) = \(\dfrac{16}{15}\)

\(\dfrac{HeLp}{me}\) \(\dfrac{nguyễn}{đức}{Trí}\)

Answer 1

\(\dfrac{4}{3.5}+\dfrac{8}{5.9}+\dfrac{12}{9.15}+...+\dfrac{32}{x\left(x+16\right)}=\dfrac{16}{15}\)

\(2.\left(\dfrac{2}{3.5}+\dfrac{4}{5.9}+\dfrac{6}{9.15}+..+\dfrac{16}{X.\left(X+16\right)}\right)=\dfrac{16}{15}\)

\(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{15}+...+\dfrac{1}{X}-\dfrac{1}{X+16}=\dfrac{8}{15}\)

\(\dfrac{1}{X+16}=\dfrac{1}{3}-\dfrac{8}{15}\)

\(\dfrac{1}{X+16}=\dfrac{-1}{5}\)

\(X+16=-5\)

\(X=-21\)