Question

Tính nhanh:

\(\dfrac{2}{3}\) + \(\dfrac{2}{15}\) + \(\dfrac{2}{35}\) + \(\dfrac{2}{63}\) + \(\dfrac{2}{99}\) + \(\dfrac{2}{143}\) .

Answer 1

Giải:

\(\dfrac{2}{3}+\dfrac{2}{15}+\dfrac{2}{35}+\dfrac{2}{63}+\dfrac{2}{99}+\dfrac{2}{143}\) 

\(=\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}+\dfrac{2}{11.13}\) 

\(=\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{13}\) 

\(=\dfrac{1}{1}-\dfrac{1}{13}\) 

\(=\dfrac{12}{13}\) 

Chúc em học tốt!

Answer 2

2/3+2/15+2/35+2/63+2/99+2/143

=2(1/1x3+1/3x5+1/5x7+1/7x9+1/9x11+1/11x13)

=2(1-1/3+1/3-1/5+1/5-....+1/13)

=2(1-1/13)

=2.12/13=24/13