Question

(1/24.25+1/25.26+....+1/29.30).120+x=1/3

Answer 1

\(120\left(\dfrac{1}{24.25}+\dfrac{1}{25.26}+...+\dfrac{1}{29.30}\right)+x=\dfrac{1}{3}\)

\(\Rightarrow120\left(\dfrac{1}{24}-\dfrac{1}{25}+\dfrac{1}{25}+\dfrac{1}{26}+...+\dfrac{1}{29}-\dfrac{1}{30}\right)+x=\dfrac{1}{3}\)

\(\Rightarrow120\left(\dfrac{1}{24}-\dfrac{1}{30}\right)+x=\dfrac{1}{3}\)

\(\Rightarrow120.\dfrac{1}{120}+x=\dfrac{1}{3}\)

\(\Rightarrow1+x=\dfrac{1}{3}\)

\(\Rightarrow x=-\dfrac{2}{3}\)