Cho B=\(\dfrac{1}{5^2}+\dfrac{2}{5^3}+\dfrac{3}{5^4}+...+\dfrac{2014}{5^{2015}}\). Chứng tỏ rằng B<\(\dfrac{1}{16}\)
chứng minh rằng
\(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{100}}\) và B= 2
so sánh
A = \(\dfrac{1}{2}.\dfrac{3}{4}.\dfrac{5}{6}...\dfrac{99}{100}\)và \(B=\dfrac{1}{10}\)
mấy bạn ơi giúp mình câu này với
chứng minh rằng: \(\dfrac{1}{2^2}+\dfrac{1}{4^2}+\dfrac{1}{6^2}+...+\dfrac{1}{4010^2}< \dfrac{1}{2}\)
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 minh rằng :
\(1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{200}>\dfrac{25}{12}\)
Cho A = \(\dfrac{1}{4}\)+\(\dfrac{1}{9}\)+\(\dfrac{1}{16}\)+....+\(\dfrac{1}{81}\)+\(\dfrac{1}{100}\) chứng tỏ rằng A > \(\dfrac{65}{132}\)
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) \(\dfrac{1}{2.4}+\dfrac{1}{4.6}+...+\dfrac{1}{96.98}\)