Question

1) Tính

B=(1+\(\dfrac{1}{2}\)).(1+\(\dfrac{1}{3}\)).(\(1+\dfrac{1}{4}\)).....(\(1+\dfrac{1}{99}\))

Answer 1

\(B=\left(1+\dfrac{1}{2}\right).\left(1+\dfrac{1}{3}\right).\left(1+\dfrac{1}{4}\right)......\left(1+\dfrac{1}{99}\right)\)

\(B=\left(\dfrac{2}{2}+\dfrac{1}{2}\right).\left(\dfrac{3}{3}+\dfrac{1}{3}\right).\left(\dfrac{4}{4}+\dfrac{1}{4}\right)......\left(\dfrac{99}{100}+\dfrac{1}{99}\right)\)

\(B=\dfrac{3}{2}.\dfrac{4}{3}.\dfrac{5}{4}......\dfrac{100}{99}=\dfrac{100}{2}=50\)