Question

1/1*3+1/3*5+1/5*7+1/7*9+...+1/19*21

Answer 1

\(\frac{1}{1.3}\)+\(\frac{1}{3\cdot5}\)+................+\(\frac{1}{19.21}\)

Đặt A = \(\frac{1}{1.3}\)+\(\frac{1}{3\cdot5}\)+.............+\(\frac{1}{19.21}\)

Nhân cả 2 vế của A với 2 ta có :

2A = \(\frac{2}{1.3}\)+\(\frac{2}{3.5}\)+............+\(\frac{2}{19.21}\)

2A = \(\frac{1}{1}\)-\(\frac{1}{3}\)+ \(\frac{1}{3}\) -  \(\frac{1}{5}\)+ ............ + \(\frac{1}{19}\)- \(\frac{1}{21}\)

2A = \(\frac{1}{1}\)- \(\frac{1}{21}\)

2A = \(\frac{20}{21}\)

  A = \(\frac{20}{21}\): 2 

  A = \(\frac{10}{21}\)