Question

Tính:

I=(\(\dfrac{1}{2}\)-\(\dfrac{1}{3}\)).(\(\dfrac{1}{2}\)-\(\dfrac{1}{5}\)).(\(\dfrac{1}{2}\)-\(\dfrac{1}{7}\)). ... .(\(\dfrac{1}{2}\)-\(\dfrac{1}{99}\))

Answer 1

\(I=\left(\dfrac{1}{2}-\dfrac{1}{3}\right)\left(\dfrac{1}{2}-\dfrac{1}{5}\right)...\left(\dfrac{1}{2}-\dfrac{1}{99}\right)\)

\(=\dfrac{1}{2}\left(1-\dfrac{1}{3}\right)\dfrac{1}{2}\left(1-\dfrac{1}{5}\right)...\dfrac{1}{2}\left(1-\dfrac{1}{99}\right)\)

Ta có:

\(\left(99-3\right):2+1=49\left(sốhạng\right)\)

\(I=\dfrac{49}{2}.\left(\dfrac{1}{3}.\dfrac{3}{5}....\dfrac{97}{99}\right)\)

\(=\dfrac{49}{2}.\dfrac{1}{99}=\dfrac{49}{198}\)