P=2/3+14/15+34/35+62/63+98/99 tính nhanh

`P=`$\dfrac{2}{3}$`+`$\dfrac{14}{15}$`+`$\dfrac{34}{35}$`+`$\dfrac{62}{63}$`+`$\dfrac{98}{99}$

`=`$\left(1-\dfrac{1}{3}\right)$`+`$\left(1-\dfrac{1}{15}\right)$`+`$\left(1-\dfrac{1}{35}\right)$`+`$\left(1-\dfrac{1}{63}\right)$`+`$\left(1-\dfrac{1}{99}\right)$

`=(1+1+1+1+1)-`$\left(\dfrac{1}{3}+\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}\right)$

`=5-`$\dfrac{1}{2}$`xx`$\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}\right)$

`=5-`$\dfrac{1}{2}$`xx`$\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{11}\right)$

`=5-`$\dfrac{1}{2}$`xx`$\left(1-\dfrac{1}{11}\right)$

`=`$\dfrac{55}{11}$`-`$\dfrac{5}{11}$

`=`$\dfrac{50}{11}$

Vậy `P=`$\dfrac{50}{11}$

`P=2/3+{14}/{15}+{34}/{35}+{62}/{63}+{98}/{99}`

`=1-1/3+1-1/{15}+1-1/{35}+1-1/{63}+1-1/{99}`

`=(1+1+1+1+1)-(1/3+1/{15}+1/{35}+1/{63}+1/{99})`

`=5-1/2xx(2/{1xx3}+2/{3xx5}+2/{5xx7}+2/{7xx9}+2/{9xx11})`

`=5-1/2xx(1/1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/{11})`

`=5-1/2xx(1-1/11)`

`=5-1/2xx{10}/{11}`

`=5-5/{11}`

`={50}/{11}`