Question

Rút gọn biểu thức sau:

T = (\(\dfrac{1}{2}+1\)) . (\(\dfrac{1}{3}+1\)) . (\(\dfrac{1}{4}+1\)) ... . (\(\dfrac{1}{98}+1\)) . (\(\dfrac{1}{99}+1\)).

Answer 1

Ta có:

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

\(=\dfrac{3}{2}.\dfrac{4}{3}.\dfrac{5}{4}.\dfrac{6}{5}.\dfrac{7}{6}...\dfrac{99}{98}.\dfrac{100}{99}\)

\(=\dfrac{3.4.5.6.7...99.100}{2.3.4.5.6...98.99}\)

\(=\dfrac{\left(3.4.5.6.7...99\right).100}{2.\left(3.4.5.6...98.99\right)}\)

\(=\dfrac{100}{2}=50\)

Vậy \(T=50\)

Answer 2

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

\(T=\dfrac{3}{2}.\dfrac{4}{3}.\dfrac{5}{4}.\dfrac{6}{5}.....\dfrac{100}{99}=\dfrac{100}{2}=50\)