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\(\frac{1}{99.97}-\frac{1}{97.95}-\frac{1}{95.93}-\frac{1}{5.3}-\frac{1}{3.1}\)
\(=\frac{1}{2}.\left(\frac{2}{99.97}-\frac{2}{97.95}-\frac{2}{95.93}-\frac{2}{5.3}-\frac{2}{3.1}\right)\)
\(=\frac{1}{2}.\left(\frac{99-97}{99.97}-\frac{97-95}{97.95}-\frac{95-93}{95.93}-\frac{5-3}{5.3}-\frac{3-1}{3.1}\right)\)
\(=\frac{1}{2}.\left[\left(\frac{99}{99.97}-\frac{97}{99.97}\right)-\left(\frac{97}{97.95}-\frac{95}{97.95}\right)-\left(\frac{95}{95.93}-\frac{93}{95.93}\right)-\left(\frac{5}{5.3}-\frac{3}{5.3}\right)-\left(\frac{3}{3.1}-\frac{1}{3.1}\right)\right]\)
\(=\frac{1}{2}.\left[\left(\frac{1}{97}-\frac{1}{99}\right)-\left(\frac{1}{95}-\frac{1}{97}\right)-\left(\frac{1}{93}-\frac{1}{95}\right)-\left(\frac{1}{3}-\frac{1}{5}\right)-\left(\frac{1}{1}-\frac{1}{3}\right)\right]\)
\(=\frac{1}{2}.\left[\frac{1}{97}-\frac{1}{99}-\frac{1}{95}+\frac{1}{97}-\frac{1}{93}+\frac{1}{95}-\frac{1}{3}+\frac{1}{5}-\frac{1}{1}+\frac{1}{3}\right]\)
\(=\frac{1}{2}.\left[-\frac{1}{99}-\frac{1}{93}+\frac{1}{5}-\frac{1}{1}\right]\)
A=\(\frac{1}{99.97}-\frac{1}{97.95}-\frac{1}{95.93}-....-\frac{1}{5.3}-\frac{1}{3.1}\) giải chi tiết
a)\(\frac{1}{99.97}\)−\(\frac{1}{97.95}\)−\(\frac{1}{95.93}\)−…−\(\frac{1}{5.3}\)−\(\frac{1}{3.1}\)
=\(\frac{1}{99.97}\)−(\(\frac{1}{97.95}\)+\(\frac{1}{95.93}\)+…+\(\frac{1}{5.3}\)+\(\frac{1}{3.1}\))
=\(\frac{1}{99.97}\)−\(\frac{1}{2}\).(\(\frac{1}{95}\)−\(\frac{1}{97}\)+\(\frac{1}{93}\)−\(\frac{1}{95}\)+…+\(\frac{1}{3}\)−\(\frac{1}{5}\)+1−\(\frac{1}{3}\))
=\(\frac{1}{99.97}\)−\(\frac{1}{2}\).(1−\(\frac{1}{97}\))
=\(\frac{1}{99.97}\)−\(\frac{1}{2}\).\(\frac{96}{97}\)
=\(\frac{1}{99.97}\)−\(\frac{48}{97}\)
=\(\frac{1}{99.97}\)−\(\frac{48.99}{99.97}\)
=\(\frac{-4751}{9603}\)
\(\frac{1}{99.97}-\frac{1}{97.95}-........-\frac{1}{5.3}-\frac{1}{3.1}\)
\(=-\left(-\frac{1}{99.97}+\frac{1}{97.95}+.........+\frac{1}{5.3}+\frac{1}{3.1}\right)\)
\(=-\left(-\frac{1}{99.97}+\frac{1}{97.95}+.......+\frac{1}{5.3}+\frac{1}{3.1}\right).\frac{2}{2}\)
\(=-\left(-\frac{2}{99.97}+\frac{2}{97.95}+......+\frac{2}{5.3}+\frac{2}{3.1}\right).\frac{1}{2}\)
\(=-\left(-\frac{1}{99}-\frac{1}{97}+\frac{1}{97}-\frac{1}{95}+.....+\frac{1}{5}-\frac{1}{3}+\frac{1}{3}-1\right).\frac{1}{2}\)
\(=\left(\frac{1}{99}-1\right).\frac{1}{2}\)
\(=-\frac{98}{99}.\frac{1}{2}\)
\(=-\frac{49}{99}\)
Đặt: \(A=\frac{1}{99.97}-\frac{1}{97.95}-\frac{1}{95.93}-...-\frac{1}{5.3}-\frac{1}{3.1}\)
\(=\frac{1}{99.97}-\left(\frac{1}{97.95}+\frac{1}{95.93}+...+\frac{1}{3.1}\right)\)
\(=\frac{1}{2}\left(\frac{1}{97}-\frac{1}{99}\right)-\frac{1}{2}\left(1-\frac{1}{3}+...+\frac{1}{93}-\frac{1}{95}+\frac{1}{95}-\frac{1}{97}\right)\)
\(=\frac{1}{2}\left(\frac{1}{97}-\frac{1}{99}\right)-\frac{1}{2}\left(1-\frac{1}{97}\right)\)
\(=\frac{1}{2}.\frac{1}{97}-\frac{1}{2}.\frac{1}{99}-\frac{1}{2}+\frac{1}{2}.\frac{1}{97}\)
\(=-\frac{4751}{9603}\)
Vậy ....
\(\frac{1}{99.97}-\frac{1}{97.95}-...-\frac{1}{5.3}-\frac{1}{3.1}\)
\(=\frac{1}{99.97}-\left(\frac{1}{97.95}+...+\frac{1}{5.3}+\frac{1}{3.1}\right)\)
\(=\frac{1}{99.97}-\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{95.97}\right)\left(1\right).\)
Đặt \(A=\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{95.97}\)
\(\Rightarrow A=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{95.97}\right)\)
\(\Rightarrow A=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{95}-\frac{1}{97}\right)\)
\(\Rightarrow A=\frac{1}{2}.\left(1-\frac{1}{97}\right)\)
\(\Rightarrow A=\frac{1}{2}.\frac{96}{97}\)
\(\Rightarrow A=\frac{48}{97}.\)
+ Thay A vào \(\left(1\right)\) ta được:
\(\frac{1}{99.97}-\frac{48}{97}\)
\(=\frac{1}{99.97}-\frac{48.99}{99.97}\)
\(=\frac{1-48.99}{99.97}\)
\(=-\frac{4751}{9603}.\)
Vậy \(\frac{1}{99.97}-\frac{1}{97.95}-\frac{1}{95.93}-...-\frac{1}{5.3}-\frac{1}{3.1}=-\frac{4751}{9603}.\)
Chúc bạn học tốt!
\(\frac{1}{99.97}-\frac{1}{97.95}-\frac{1}{95.93}-...-\frac{1}{5.3}-\frac{1}{3.1}.\)
\(=\frac{1}{99.97}-\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{93.95}+\frac{1}{95.97}\right)\)
\(=\frac{1}{99.97}-\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{93.95}+\frac{2}{95.97}\right)\)
\(=\frac{1}{99.97}-\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...-\frac{1}{95}+\frac{1}{95}-\frac{1}{97}\right)\)
\(=\frac{1}{99.97}-\frac{1}{2}\left(1-\frac{1}{97}\right)=\frac{1}{99.97}-\frac{1}{2}.\frac{96}{97}\)
\(=\frac{1}{99.97}-\frac{48}{97}\)
chúc bạn học tốt
\(\frac{1}{99.97}-\frac{1}{97.95}-\frac{1}{95.93}-...-\frac{1}{5.3}-\frac{1}{3.1}\)
\(=\frac{1}{99.97}-\left(\frac{1}{97.95}+\frac{1}{95.93}+...+\frac{1}{5.3}+\frac{1}{3.1}\right)\)
\(=\frac{1}{99.97}-\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{93}-\frac{1}{95}+\frac{1}{95}-\frac{1}{97}\right)\)
\(=\frac{1}{99.97}-\frac{1}{2}\left(1-\frac{1}{97}\right)\)
\(=\frac{1}{99.97}-\frac{48}{97}\)
\(=-\frac{4751}{9603}\)
hình như làm nhầm r xin lỗi nha! làm lại
1/2(1/(99*97))-1/2(-1/97+1/95-1/95+1/93...+1)=1/2(1/(99*97))-1/2(-1/97+1)=-9503/19206
lần này hi vọng ko nhầm
Tôi thấy bài này nó cứ sai sai
Ở chỗ \(\frac{1}{99.97}-\frac{1}{97.95}\)í
\(\frac{1}{97.95}>\frac{1}{99.97}\)mà ông Thám Tử THCS Nguyễn Hiếu CTV
violympic cho sai đề :
Đề đúng là tính : \(A=\frac{1}{99.97}-\frac{1}{97.95}-\frac{1}{95.53}-....-\frac{1}{5.3}-\frac{1}{3.1}\)
Làm theo đề đúng !! ok
Ta có : \(A=\frac{1}{99.97}-\left(\frac{1}{97.95}+\frac{1}{95.53}+....+\frac{1}{5.3}+\frac{1}{3.1}\right)\)
\(=\frac{1}{99.97}-\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+....+\frac{1}{95}-\frac{1}{97}\right)\)
\(=\frac{1}{99.97}-\frac{1}{2}\left(1-\frac{1}{97}\right)=\frac{1}{99.97}-\frac{48}{97}=-\frac{4751}{9603}\)