\(A=\left(\dfrac{1}{2}+1\right)\left(\dfrac{1}{3}+1\right)\left(\dfrac{1}{4}+1\right)...\left(\dfrac{1}{99}+1\right)\)
\(=\dfrac{3}{2}.\dfrac{4}{3}.\dfrac{5}{4}...\dfrac{100}{99}=\dfrac{100}{2}=50\)
Vậy A = 50
Ta có:
A=\(^{\left(\dfrac{1}{2}+1\right).\left(\dfrac{1}{3}+1\right).\left(\dfrac{1}{4}+1\right).....\left(\dfrac{1}{99}\right)+1}\)
A= \(\dfrac{3}{2}.\dfrac{4}{3}.\dfrac{5}{4}.....\dfrac{1}{99}+1\)
A=\(\dfrac{1}{2}+1\)
A=\(\dfrac{3}{2}\)
Giải:
\(A=\left(\dfrac{1}{2}+1\right)\left(\dfrac{1}{3}+1\right)\left(\dfrac{1}{4}+1\right).....\left(\dfrac{1}{99}+1\right).\)
\(A=\left(\dfrac{1}{2}+\dfrac{2}{2}\right)\left(\dfrac{1}{3}+\dfrac{3}{3}\right)\left(\dfrac{1}{4}+\dfrac{4}{4}\right).....\left(\dfrac{1}{99}+\dfrac{99}{99}\right).\)
\(A=\dfrac{3}{2}.\dfrac{4}{3}.\dfrac{5}{4}.....\dfrac{100}{99}.\)
\(A=\dfrac{3.4.5.....100}{2.3.4.....99}.\)
\(A=\dfrac{100}{2}.\) (dùng tính chất rút gọn của phân số).
\(A=50.\)
Vậy \(A=50.\)
~ Học tốt!!! ... ~
\(A=\left(\dfrac{1}{2}+1\right)\left(\dfrac{1}{3}+1\right)\left(\dfrac{1}{4}+1\right)...\left(\dfrac{1}{99}+1\right)\)
\(A=\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot\dfrac{5}{4}\cdot...\cdot\dfrac{100}{99}\)
\(A=\dfrac{3\cdot4\cdot5\cdot...\cdot100}{2\cdot3\cdot4\cdot...\cdot99}\)
\(A=\dfrac{100}{2}=50\)
A=(\(\dfrac{1}{2}\)+1)(\(\dfrac{1}{3}\)+1)(\(\dfrac{1}{4}\)+1).......(\(\dfrac{1}{99}\))+1
A=\(\dfrac{3}{2}\).\(\dfrac{4}{3}\).\(\dfrac{5}{4}\)......\(\dfrac{1}{99}\)+1
A=\(\dfrac{3.4.5.6....1}{2.4.5.6...99}\)+1
A=\(\dfrac{1}{2.99}\)+1
A=\(\dfrac{1}{198}\)+1
A=\(\dfrac{199}{198}\)
