Question

15/90.94 + 15/94.98 + 15/98.102 +...+15/146.150

Answer 1

\(\dfrac{15}{90\cdot94}+\dfrac{15}{94\cdot98}+\dfrac{15}{98\cdot102}+...+\dfrac{15}{146\cdot150}\)

\(=\dfrac{15}{4}\left(\dfrac{4}{90\cdot94}+\dfrac{4}{94\cdot98}+...+\dfrac{4}{146\cdot150}\right)\)

\(=\dfrac{15}{4}\left(\dfrac{1}{90}-\dfrac{1}{94}+\dfrac{1}{94}-\dfrac{1}{98}+...+\dfrac{1}{146}-\dfrac{1}{150}\right)\)

\(=\dfrac{15}{4}\left(\dfrac{1}{90}-\dfrac{1}{150}\right)=\dfrac{15}{4}\cdot\dfrac{1}{225}=\dfrac{1}{60}\)