tinh 1^1^2.1^1^3.1^1^4.....1^1^98.1^1^99
Những câu hỏi liên quan
tinh nhanh
1/2.1/-3+1/-3.1/4+1/4.1/-5+1/-5.1/6
1^2.1^3.1^4........1^99
giúp mình giải bài toán nha mn
nhớ ghi từng bước ra nha
Tính nhanh
a) -1/20-1/20.19-1/19.18-...-1/2.1
b 1/99- 1/99.97-1/97.95-..-1/3.1
Ai TL đúng mình sẽ tick ạ
a, \(A=-\dfrac{1}{20}-\left(\dfrac{1}{20\cdot19}+\dfrac{1}{19\cdot18}+...+\dfrac{1}{2\cdot1}\right)\\ \Rightarrow A=-\dfrac{1}{20}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{19}-\dfrac{1}{20}\right)\\ \Rightarrow A=-\dfrac{1}{20}-1+\dfrac{1}{20}=-1\)
b, \(B=\dfrac{1}{99}-\dfrac{1}{99\cdot97}-\dfrac{1}{97\cdot95}-...-\dfrac{1}{3\cdot1}\\ \Rightarrow B=\dfrac{1}{99}-\dfrac{1}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{97\cdot99}\right)\\ \Rightarrow B=\dfrac{1}{99}-\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{97}-\dfrac{1}{99}\right)\\ \Rightarrow B=\dfrac{1}{99}-\dfrac{1}{2}+\dfrac{1}{2\cdot99}=-\dfrac{16}{33}\)
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1/2.1/3+1/3.1/4+1/4.....1/19.1/20
1/2.1/3+1/3.1/4...........1/19/1/20
=1/2-1/20
=9/20
ok
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vinh dư
A=1/-2.1/3+1/-3.1/4+....+1/-9.10
tính A
\(A=-\dfrac{1}{2.3}-\dfrac{1}{3.4}-\dfrac{1}{4.5}-...-\dfrac{1}{9.10}\)
\(\Rightarrow-A=\dfrac{3-2}{2.3}+\dfrac{4-3}{3.4}+\dfrac{5-4}{4.5}+...+\dfrac{10-9}{9.10}=\)
\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{10}=\)
\(=\dfrac{1}{2}-\dfrac{1}{10}=\dfrac{2}{5}\Rightarrow A=-\dfrac{2}{5}\)
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tính hợp A=1/2+1/3-1/4:(1/2+1/3-1/4)-1/2.1/3.1/4
1/2.1/-3+1/-3.1/4+1/4.1/-5+1/-5.1/6 = ?
=-1/2.3-1/3.4-1/4.5-1/5.6
=-(1/2.3+1/3.4+1/4.5+1/5.6)
=-(1/2-1/3+1/3-1/4+1/5-1/6)
=-(1/2-1/6)
=1/6-1/2=-1/3
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3x.(1/1.1/2+1/2.1/3+1/3.1/4+1/4.1/5+1/5.1/6)=3/4
tính nhanh
1/2.1/2+1/2.1/3+1/3.1/4+1/4.1/5+1/5.1/6
Lời giải rõ ràng nha mọi người
\(\frac{1}{2}.\frac{1}{2}+\frac{1}{2}.\frac{1}{3}\)\(+\frac{1}{3}.\frac{1}{4}+\frac{1}{4}.\frac{1}{5}+\frac{1}{5}.\frac{1}{6}\)
\(=\frac{1}{4}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\)
\(=\frac{1}{4}+\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\right)\)
\(=\frac{1}{4}+\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\right)\)
\(=\frac{1}{4}+\left(\frac{1}{2}-\frac{1}{6}\right)\)
\(=\frac{1}{4}+\frac{1}{3}\)
\(=\frac{7}{12}\)
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HINH NHU BAN VIET NHAM DAU BAI ROI
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\(\frac{1}{1}.\frac{1}{2}+\frac{1}{2}.\frac{1}{3}+\frac{1}{3}.\frac{1}{4}+\frac{1}{4}.\frac{1}{5}+\frac{1}{5}.\frac{1}{6}\)
\(=\frac{1.1}{1.2}+\frac{1.1}{2.3}+\frac{1.1}{3.4}+\frac{1.1}{4.5}+\frac{1.1}{5.6}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(=1-\frac{1}{6}\)
\(=\frac{5}{6}\)
_Chúc bạn học tốt_
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