Tuyển Cộng tác viên Hoc24 nhiệm kì 26 tại đây: https://forms.gle/dK3zGK3LHFrgvTkJ6
Cho biểu thức sau: \(P=\frac{1}{5}+\frac{2}{5^2}+\frac{3}{5^3}+\frac{4}{5^4}+.....+\frac{2015}{5^{2015}}+\frac{2016}{5^{2016}}\)
Chứng minh 1/4 < P< 1/3
Cho \(A=\frac{1}{5}+\frac{2}{5^2}+\frac{3}{5^3}+\frac{4}{5^4}+...+\frac{2015}{5^{2015}}\)
CMR a) A<1
b) A<\(\frac{1}{16}\)
Cho N=\(\frac{2}{1}.\frac{4}{3}.\frac{6}{5}...\frac{2016}{2015}\). Chứng minh rằng N<52
Cho \(B=\frac{1}{5^2}+\frac{2}{5^3}+\frac{3}{5^4}+...+\frac{2014}{5^{2015}}\)
Chứng tỏ rằng : B < \(\frac{1}{16}\)
2) \(A=\frac{3^{2017}+5}{3^{2015}+5}vàB=\frac{3^{2015}+1}{3^{2013}+1}\)so sánh A,B
Cho \(B=\frac{1}{5^2}+\frac{2}{5^3}+\frac{3}{5^4}+...+\frac{2014}{5^{2015}}.\)Chứng tỏ rằng B<\(\frac{1}{16}\)
2,Cho A=9999932015 - 5555572013
chứng minh A chia hết cho 5
3, c/m \(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}<\frac{1}{3}\)
Tính tổng
\(A=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{100}\)
\(B=\frac{2}{3}+\frac{3}{4}+\frac{4}{5}+...+\frac{2015}{2016}\)
