1. Chứng tỏ rằng:
a) \(\dfrac{1}{a.\left(a+1\right)}=\dfrac{1}{a}-\dfrac{1}{a+1}\)
b) \(\dfrac{m}{a.\left(a+m\right)}=\dfrac{1}{a}-\dfrac{1}{a+m}\)
2. Tính
a) \(\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\)
b) \(\dfrac{5}{10.15}+\dfrac{5}{15.20}+...+\dfrac{5}{195.200}\)
c) \(\dfrac{1}{2.4}+\dfrac{1}{4.6}+...+\dfrac{1}{96.98}\)
sắp xếp các phân số theo thứ tự
a) Tăng dần: \(\dfrac{-5}{6}\);\(\dfrac{7}{8};\dfrac{7}{24};\dfrac{16}{17};\dfrac{-3}{4};\dfrac{2}{3}\)
b) Giảm dần: \(\dfrac{-5}{8};\dfrac{7}{10};\dfrac{-16}{19};\dfrac{20}{23};\dfrac{214}{315};\dfrac{205}{107}\)
Tìm x biết
a) \(\dfrac{x}{3}=\dfrac{7}{25}+\dfrac{-1}{5}\)
b)\(\dfrac{4}{9}+\dfrac{x}{5}=\dfrac{5}{11}\)
c) \(\dfrac{-5}{9}+\dfrac{x}{10}=\dfrac{1}{3}\)
so sánh
A = \(\dfrac{1}{2}.\dfrac{3}{4}.\dfrac{5}{6}...\dfrac{99}{100}\)và \(B=\dfrac{1}{10}\)
Cho:\(A=\dfrac{1}{3^2}+\dfrac{1}{5^2}+\dfrac{1}{7^2}+...+\dfrac{1}{99^2}.Cm:\dfrac{1}{5}< A< \dfrac{1}{4}\)
chứng tỏ rằng:
E=\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{100^2}\)<\(\dfrac{3}{4}\)
mấy bạn ơi giúp mình câu này
a) \(\dfrac{-3}{5}\) và \(\dfrac{39}{-65}\) c)\(\dfrac{-3}{4}\) và \(\dfrac{4}{-5}\)
b) \(\dfrac{-9}{27}\)và \(\dfrac{-41}{123}\) d)\(\dfrac{2}{-3}\) và \(\dfrac{-5}{7}\)
ko quy đồng hãy so sánh
a) A=\(\dfrac{3}{8^3}\)+\(\dfrac{7}{8^4}\)
B=\(\dfrac{7}{8^3}\)+\(\dfrac{4}{8^4}\)
b)A= \(\dfrac{5^{12}+1}{5^{13}+1}\)
B=\(\dfrac{5^{11}+1}{5^{12}+1}\)