CMR:
\(\frac{1}{3}-\frac{2}{3^2}+\frac{3}{3^3}-\frac{4}{3^4}+...-\frac{2014}{3^{2014}}<\frac{1}{5}\)
a) Cho tổng gồm 2014 số hạng
S= \(\frac{1}{4}+\frac{2}{4^2}+\frac{3}{4^3}+\frac{4}{4^4}+...+\frac{2014}{4^{2014}}\)
CMR S<1
\(S=1+\frac{2}{2}+\frac{3}{2^2}+\frac{4}{2^3}+...+\frac{2014}{2^{2013}}+\frac{2015}{2^{2014}}\)cmr S<4
Chứng minh: \(\frac{1}{3}-\frac{2}{3^2}+\frac{3}{3^3}-\frac{4}{3^4}+...-\frac{2014}{3^{2014}}<\frac{1}{5}\)
cmr S<1/2 khi S = \(\frac{1}{4}+\frac{2}{4^2}+\frac{3}{4^3}+...+\frac{2014}{4^{2014}}\)
Chứng minh:
\(\frac{1}{3}-\frac{2}{3^2}+\frac{3}{3^3}-\frac{4}{3^4}+...-\frac{2014}{3^{2014}}<\frac{1}{5}\)
Chứng minh: \(A=\frac{1}{3}-\frac{2}{3^2}+\frac{3}{3^3}-\frac{4}{3^4}+...-\frac{2014}{3^{2014}}<\frac{1}{5}\)
Cho tổng gồm 2014 số hạng: S= \(\frac{1}{4}+\frac{2}{4^2}+\frac{3}{4^3}+...+\frac{2014}{4^{2014}}\).CMR: S<\(\frac{1}{2}\)
So sánh S với \(\frac{1}{3}\)biết: \(S=\frac{1}{5}+\frac{2}{5^2}+\frac{3}{5^3}+\frac{4}{5^4}+...........+\frac{2014}{5^{2014}}.\)
