\(=\dfrac{1}{8}\left(1+\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}\right)\)
\(=\dfrac{1}{8}\cdot2\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}\right)\)
\(=\dfrac{1}{4}\cdot\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{6}-\dfrac{1}{7}\right)\)
\(=\dfrac{1}{4}\cdot\dfrac{6}{7}=\dfrac{3}{14}\)
Tính nhanh
A=1+\(\dfrac{1}{8}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{80}+\dfrac{1}{120}\)
TÍNH NHANH:
A=\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{9900}\)
B=\(\dfrac{1}{3}+\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{63}+...+\dfrac{1}{95}\)
C=\(\dfrac{1}{8}+\dfrac{1}{24}+\dfrac{1}{48}+...+\dfrac{1}{9800}\)
*D=\(\dfrac{2}{3.5}+\dfrac{3}{5.8}+\dfrac{11}{8.19}+\dfrac{13}{19.32}+\dfrac{25}{32.57}+\dfrac{30}{57.87}\)
Điền dấu thích hợp ( >, <, =) vào ô vuông :
a) \(\dfrac{-4}{7}+\dfrac{3}{-7}.......-1\)
b) \(\dfrac{-15}{22}+\dfrac{-3}{22}......\dfrac{-8}{11}\)
c) \(\dfrac{3}{5}.....\dfrac{2}{3}+\dfrac{-1}{5}\)
d) \(\dfrac{1}{6}+\dfrac{-3}{4}.......\dfrac{1}{14}+\dfrac{-4}{7}\)
Cộng các phân số (rút gọn kết quả nếu có thể)
a) \(\dfrac{1}{-5}+\dfrac{-5}{8}\)
b) \(\dfrac{4}{13}+\dfrac{-12}{39}\)
c) \(\dfrac{-1}{21}+\dfrac{-1}{28}\)
Cộng các phân số (rút gọn kết quả nếu có thể)
a) \(\dfrac{7}{-25}+\dfrac{-8}{25}\)
b) \(\dfrac{1}{6}+\dfrac{-5}{6}\)
c) \(\dfrac{6}{13}+\dfrac{-14}{39}\)
d) \(\dfrac{4}{5}+\dfrac{4}{-18}\)
Số giá trị x∈Z , thỏa mãn 1+\(\dfrac{-1}{60}\)+\(\dfrac{19}{120}\)<\(\dfrac{x}{36}\)+\(\dfrac{-1}{60}\)<\(\dfrac{58}{90}\)+\(\dfrac{59}{72}\)+\(\dfrac{-1}{60}\) là :
Tính A =\(\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}+\dfrac{1}{28}+\dfrac{1}{36}+\dfrac{1}{45}+\dfrac{1}{55}+\dfrac{1}{66}+\dfrac{1}{78}\)
thực hiện phép tính bằng cách hợp lí:
1,A=\(\dfrac{1}{2\cdot3}\)+\(\dfrac{1}{3\cdot4}\)+\(\dfrac{1}{4\cdot5}\)+...+\(\dfrac{1}{99\cdot100}\)
2,B=\(\dfrac{1}{30}\)+\(\dfrac{1}{42}\)+\(\dfrac{1}{56}\)+\(\dfrac{1}{72}\)+\(\dfrac{1}{30}\)+\(\dfrac{1}{110}\)+\(\dfrac{1}{132}\)
\(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+....+\dfrac{1}{99}+\dfrac{1}{x.\left(x+1\right)}=\dfrac{1}{2001}\)
