\(C=\frac{5}{4}+\frac{5}{4^2}+\frac{5}{4^3}+...+\frac{5}{4^{99}}\)
\(4C=5+\frac{5}{4}+\frac{5}{4^2}+\frac{5}{4^3}+...+\frac{5}{4^{98}}\)
\(4C-C=\left(5+\frac{5}{4}+...+\frac{5}{4^{98}}\right)-\left(\frac{5}{4}+\frac{5}{4^2}+...+\frac{5}{4^{99}}\right)\)
\(3C=5-\frac{5}{4^{99}}\)
\(C=\frac{5-\frac{5}{4^{99}}}{3}\)
\(C=\frac{5}{3}-\frac{5}{4^{99}.3}< C\)
đpcm
Cho C = \(\frac{5}{4}+\frac{5}{4^2}+\frac{5}{4^3}+...+\frac{5}{4^{99}}.\)Chứng minh rằng C <\(\frac{5}{3}\)
Cho C= \(\frac{5}{4}+\frac{5}{4^2}+\frac{5}{4^3}+..+\frac{5}{4^{99}}\) Chứng minh C<5/3
Cho C =\(\frac{5}{4}+\frac{5}{4^2}+\frac{5}{4^3}+...+\frac{5}{4^{99}}\)
Chứng minh C <\(\frac{5}{3}\)
Cho S=\(\frac{1}{5^2}-\frac{2}{5^3}+\frac{3}{5^4}-\frac{4}{5^5}+...+\frac{99}{5^{100}}-\frac{100}{5^{101}}\)
Chứng minh rằng \(S< \frac{1}{36}\)
Chứng minh rằng \(D=\frac{1}{5^2}+\frac{2}{5^3}+\frac{3}{5^4}+...+\frac{99}{5^{100}}< \frac{1}{16}\)
Cho C=\(\frac{5}{4}\)+\(\frac{5}{4^2}\)+\(\frac{5}{4^3}\)+...+\(\frac{5}{4^{99}}\). Chứng minh:C<\(\frac{5}{3}\)
Chứng minh rằng :
\(100-\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}\right)=\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+\frac{4}{5}+...+\frac{99}{100}\)
Chứng minh rằng: \(\frac{200-\left(3+\frac{2}{3}+\frac{2}{4}+\frac{2}{5}+..+\frac{2}{100}\right)}{\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+...+\frac{99}{100}}=2\)
Chứng minh rằng
a) \(\frac{1}{5}<\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{98}-\frac{1}{99}<\frac{2}{5}\)
b) \(\frac{1}{15}<\frac{1}{2}.\frac{3}{4}.\frac{5}{6}...\frac{99}{100}<\frac{1}{10}\)
