Câu hỏi của Lam Thường

Question

Ai giúp tớ với:

Tính: $\frac{1}{99.97}-\frac{1}{97.95}-\frac{1}{95.93}-.....-\frac{1}{5.3}-\frac{1}{3.1}$

Nguyễn Huy Tú · Accepted Answer

$\frac{1}{99.97}-\frac{1}{97.95}-...-\frac{1}{5.3}-\frac{1}{3.1}$

$=\frac{1}{97.99}-\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{95.97}\right)$

$=\frac{1}{97.99}-\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{95.97}\right)$

$=\frac{1}{97.99}-\frac{1}{2}\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{95}-\frac{1}{97}\right)$

$=\frac{1}{9603}-\frac{1}{2}\left(1-\frac{1}{97}\right)$

$=\frac{1}{9603}-\frac{1}{2}.\frac{96}{97}$

$=\frac{-4751}{9603}$Câu trả lời: $\frac{1}{99.97}-\frac{1}{97.95}-...-\frac{1}{5.3}-\frac{1}{3.1}$

$=\frac{1}{97.99}-\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{95.97}\right)$

$=\frac{1}{97.99}-\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{95.97}\right)$

$=\frac{1}{97.99}-\frac{1}{2}\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{95}-\frac{1}{97}\right)$

$=\frac{1}{9603}-\frac{1}{2}\left(1-\frac{1}{97}\right)$

$=\frac{1}{9603}-\frac{1}{2}.\frac{96}{97}$

$=\frac{-4751}{9603}$

Vũ Thị Khánh Linh · Answer

A=-(1/99.97+1/97.95+...+1/5.3+1/3.1)

2B=2/99.97+2/97.95+...+2/5.3+2/3.1

2B=1-1/3+1/3-1/5+...+1/97-1/99

2B=1-1/99

2B=98/99

B=49/99

Suy ra A=-1/49/49