\(B=\left(1+\dfrac{1}{2}\right)\left(1+\dfrac{1}{3}\right)\left(1+\dfrac{1}{4}\right)...\left(1+\dfrac{1}{99}\right)\)
\(=\dfrac{3}{2}.\dfrac{4}{3}.\dfrac{5}{4}...\dfrac{100}{99}=\dfrac{3.4.5...100}{2.3.4...99}=\dfrac{\left(3.4.5...99\right)100}{2\left(3.4.5...99\right)}=\dfrac{100}{2}=50\)
Vậy B = 50
\(B=\left(1+\dfrac{1}{2}\right).\left(1+\dfrac{1}{3}\right).\left(1+\dfrac{1}{4}\right).....\left(1+\dfrac{1}{99}\right)\)
\(B=\dfrac{3}{2}.\dfrac{4}{3}.\dfrac{5}{4}.....\dfrac{100}{99}\)
\(B=\dfrac{3.4.5....99.100}{2.3.4....98.99}\)
\(B=\dfrac{100}{2}\)
\(B=50\)
\(B=\left(1+\dfrac{1}{2}\right)\cdot\left(1+\dfrac{1}{3}\right)\cdot\left(1+\dfrac{1}{4}\right)...\left(1+\dfrac{1}{99}\right)\\ =\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot\dfrac{5}{4}\cdot...\cdot\dfrac{100}{99}\\ =\dfrac{3\cdot4\cdot5\cdot...\cdot100}{2\cdot3\cdot4\cdot...\cdot99}\\ =\dfrac{100}{2}\\ =50\)
Ta có :
\(B=\left(1+\dfrac{1}{2}\right)\left(1+\dfrac{1}{3}\right)\left(1+\dfrac{1}{4}\right).............\left(1+\dfrac{1}{99}\right)\)
\(B=\left(\dfrac{2}{2}+\dfrac{1}{2}\right)\left(\dfrac{3}{3}+\dfrac{1}{3}\right)\left(\dfrac{4}{4}+\dfrac{1}{4}\right).............\left(\dfrac{99}{99}+\dfrac{1}{99}\right)\)
\(B=\dfrac{3}{2}.\dfrac{4}{3}.\dfrac{5}{4}.........\dfrac{100}{99}\)
\(B=\dfrac{1}{2}.\dfrac{100}{1}=50\)
~ Học tốt ~
