Question

B=(1-\(\dfrac{1}{3}\)) ✖(1-\(\dfrac{1}{6}\))✖(1-\(\dfrac{1}{10}\))✖(1-\(\dfrac{1}{15}\))✖....✖(1-\(\dfrac{1}{780}\))

 

Answer 1

\(B=\left(1-\dfrac{1}{3}\right)\cdot\left(1-\dfrac{1}{6}\right)\cdot\left(1-\dfrac{1}{10}\right)\cdot\left(1-\dfrac{1}{15}\right)\cdot...\cdot\left(1-\dfrac{1}{780}\right)\)

\(B=\left(1-\dfrac{1}{3+6+10+15+...+780}\right)\)

\(B=\left(1-\dfrac{1}{\left(780-3\right)\div3+1}\right)\)

\(B=\left(1-\dfrac{1}{260}\right)\)

\(B=\dfrac{259}{260}\)