Tính nhanh các tổng sau :
S=\(\dfrac{2}{1.3}\)+\(\dfrac{2}{3.5}+\)\(\dfrac{2}{5.7}+\)...+\(\dfrac{2}{47.49}\)
Chứng minh rằng:
\(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{\left(2n+1\right)\left(2n+3\right)}=\dfrac{n+1}{2n+3}\)
Giúp mik vs các bn
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=\(\dfrac{2}{3.5}+\dfrac{3}{5.8}+\dfrac{11}{8.19}+\dfrac{13}{19.32}+\dfrac{25}{32.57}+\dfrac{30}{57.87}\)
\(\dfrac{x}{2}\)-(\(\dfrac{3x}{5}\)-\(\dfrac{13}{5}\))=-(\(\dfrac{7}{5}\)+\(\dfrac{7}{10}\).\(x\))
\(\dfrac{2x-3}{3}\)+\(\dfrac{-3}{2}\)=\(\dfrac{5-3x}{6}\)-\(\dfrac{1}{3}\)
\(\dfrac{2}{3x}\)-\(\dfrac{3}{12}\)=\(\dfrac{4}{5}-\left(\dfrac{7}{x}-2\right)\)
bài 45: Tìm x, biết:
a) x=\(\dfrac{-1}{2}+\dfrac{3}{4}\); b) \(\dfrac{x}{5}=\dfrac{5}{6}+\dfrac{-19}{30}\)
5\(7\dfrac{3}{5}-\left(2\dfrac{5}{7}+5\dfrac{3}{5}\right)\)
\(\dfrac{-6}{7}+\dfrac{2}{5}< \dfrac{x}{5}< \dfrac{-3}{105}+\dfrac{17}{35}\)
Cộng các phân số sau :
a) \(\dfrac{1}{6}+\dfrac{2}{5}\)
b) \(\dfrac{3}{5}+\dfrac{-7}{4}\)
c) \(\left(-2\right)+\dfrac{-5}{8}\)
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) \(\dfrac{1}{6}+\dfrac{-3}{4}.......\dfrac{1}{14}+\dfrac{-4}{7}\)