Tính
A=(1-1/2).(1-1/3).(1-1/4).....(1-1/100)
B= (1+1/1.3).(1+1/2.4).(1+1/3.5).....(1+1/99.101)
Những câu hỏi liên quan
thuc hien phep cac phep tinh sau:
a, (1-1/2).(1-1/3).(1-1/4)...(1-1/100)
b, (1+1/1.3).(1+1/2.4).(1+1/3.5)...(1+1/99.101)
Bài 3 : (1+1/1.3)(1+1/2.4)(1+1/3.5)...(1+1/99.101)
bài 4:
(x-3)(x+5)/(x-2)^2 <0
\(\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right).....\left(1+\frac{1}{99.101}\right)\)
\(=\frac{2.2}{1.3}\frac{3.3}{2.4}.....\frac{100.100}{99.101}\)
\(=\frac{\left(2.3.4.....100\right).\left(2.3.4.....100\right)}{\left(1.2.3.....99\right).\left(3.4.5.....101\right)}\)
\(=\frac{100.2}{101}=\frac{200}{101}\)
\(\frac{\left(x-3\right)\left(x+5\right)}{\left(x-2\right)^2}< 0\)
\(\Rightarrow\frac{\left(x-3\right)\left(x+5\right)}{\left(x-2\right).\left(x-2\right)}< 0\)
=> ( x - 3 ) . ( x - 5 ) và ( x - 2 ) . ( x - 2 ) trái dấu
Mà ( x - 2 )2 = ( x - 2 ) . ( x - 2 ) ≥ 0 ∀ x
\(\Rightarrow\hept{\begin{cases}\left(x−3\right).\left(x+5\right)< 0\\\left(x−2\right).\left(x−2\right)>0\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x< −5;−5< x< 3\\x>2\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x< −5\\2< x< 3\end{cases}}\)
(1+1/1.3).(1+1/2.4)(1+1/3.5)....(1+1/99.101)
(1+1/1.3).(1+1/2.4).(1+1/3.5).........(1+1/99.101)
\(\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right).\left(\frac{1}{3.5.}\right).....\left(1+\frac{1}{99.101}\right)\)
\(=\frac{4}{3}.\frac{9}{8}.\frac{16}{15}.....\frac{10000}{9999}\)
\(=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}.....\frac{100^2}{99.101}\)
\(=\frac{2^2.3^2.4^2.5^2.....98^2.99^2.100^2}{1.2.3^2.4^2.5^2......99^2.100.101}\)
\(=\frac{2.100}{1.101}\)
\(=\frac{200}{101}\)
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(1+1/1.3)(1+1/2.4)(1+1/3.5)...(1/1+1/99.101)
A=(1+1/1.3).(1+1/2.4).(1+1/3.5).....(1+1/99.101)
\(A=\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)\left(1+\frac{1}{3.5}\right).....+\left(1+\frac{1}{99.101}\right)\)
\(=\frac{1.3+1}{1.3}.\frac{2.4+1}{2.4}.\frac{3.5+1}{3.5}.....\frac{99.101+1}{99.101}\)
\(=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}.....\frac{100^2}{99.101}\)
\(=\frac{2.3.4.....100}{1.2.3.....99}.\frac{2.3.4.....100}{3.4.5.....101}\)
\(=100.\frac{2}{101}=\frac{200}{101}\)
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Tính H = (1 + 1/1.3)(1 + 1/2.4)(1 + 1/3.5)...(1+1/99.101)
V=(1+1/1.3).(1+1/2.4).(1+1/3.5)....(1+1/99.101)
Tính nhanh
Tính
D=(1+1/1.3)(1+1/2.4)(1+1/3.5).............(1+1/99.101)
\(\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)...\left(1+\frac{1}{99.101}\right)\)
\(=\frac{4}{1.3}.\frac{9}{2.4}....\frac{10000}{99.101}\)
\(=\frac{2.2.3.3...100.100}{1.3.2.4...99.101}\)
\(=\frac{\left(2.3.4...100\right)\left(2.3.4...100\right)}{\left(1.2...99\right)\left(3.4.5...101\right)}\)
\(=\frac{100.2}{101}=\frac{200}{101}\)
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\(D=\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)\left(1+\frac{1}{3.5}\right)...\left(1+\frac{1}{99.101}\right)\)
\(D=\frac{4}{1.3}.\frac{9}{2.4}.\frac{16}{3.5}...\frac{10000}{99.101}\)
\(D=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}...\frac{100^2}{99.101}\)
\(D=\frac{2.3.4...100}{1.2.3...99}.\frac{2.3.4...100}{3.4.5...101}=100.\frac{2}{101}=\frac{200}{101}\)
Vậy \(D=\frac{200}{101}\)