giúp em với \(\dfrac{1}{1^2}+\dfrac{1}{2^2}+\dfrac{1}{3^2}+.........+\dfrac{1}{2017^2}\)
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=\(\dfrac{2}{3.5}+\dfrac{3}{5.8}+\dfrac{11}{8.19}+\dfrac{13}{19.32}+\dfrac{25}{32.57}+\dfrac{30}{57.87}\)
Tìm \(x\), biết :
a) \(x=\dfrac{1}{4}+\dfrac{2}{13}\)
b) \(\dfrac{x}{3}=\dfrac{2}{3}+\dfrac{-1}{7}\)
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) \(\dfrac{1}{6}+\dfrac{-3}{4}.......\dfrac{1}{14}+\dfrac{-4}{7}\)
bài 45: Tìm x, biết:
a) x=\(\dfrac{-1}{2}+\dfrac{3}{4}\); b) \(\dfrac{x}{5}=\dfrac{5}{6}+\dfrac{-19}{30}\)
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=\(\dfrac{1}{30}\)+\(\dfrac{1}{42}\)+\(\dfrac{1}{56}\)+\(\dfrac{1}{72}\)+\(\dfrac{1}{30}\)+\(\dfrac{1}{110}\)+\(\dfrac{1}{132}\)
tìm x biết \(\dfrac{-15}{41}+\dfrac{-138}{41}\le x\le\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{6}\)
Tính tổng :
\(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{2010\cdot2011}\)
\(\dfrac{x}{2}\)-(\(\dfrac{3x}{5}\)-\(\dfrac{13}{5}\))=-(\(\dfrac{7}{5}\)+\(\dfrac{7}{10}\).\(x\))
\(\dfrac{2x-3}{3}\)+\(\dfrac{-3}{2}\)=\(\dfrac{5-3x}{6}\)-\(\dfrac{1}{3}\)
\(\dfrac{2}{3x}\)-\(\dfrac{3}{12}\)=\(\dfrac{4}{5}-\left(\dfrac{7}{x}-2\right)\)