Đặt \(A=\dfrac{100}{3}+\dfrac{100}{3^2}+\dfrac{100}{3^3}+\dfrac{100}{3^4}\)
\(3A=100+\dfrac{100}{3}+\dfrac{100}{3^2}+\dfrac{100}{3^3}\)
\(3A-A=\left(100+\dfrac{100}{3}+\dfrac{100}{3^2}+\dfrac{100}{3^3}\right)-\left(\dfrac{100}{3}+\dfrac{100}{3^2}+\dfrac{100}{3^3}+\dfrac{100}{3^4}\right)\)\(2A=100-\dfrac{100}{3^4}\)
\(A=\dfrac{100-\dfrac{100}{3^4}}{2}\)
Tính [100/3] + [100/3^2] + [100/3^3] + [100/3^4]
CMR : 1/3 - 2/3^2 + 3^3 - 4/3^4 + .... + 99/3^99 - 100/3^100 < 3/16
Chứng minh rằng 1/3 + 2/3^2 + 3/3^3 + .....+ 100/3^100 < 3/4?
tính :1*2-1/2!-3*2-1/3!+3*4-1/4!+...+99*100-1/100!
Chứng minh: \(\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+\frac{4}{3^4}+...................+\frac{100}{3^{100}}< \frac{3}{4}\)
Chứng minh: \(\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+\frac{4}{3^4}+...................+\frac{100}{3^{100}}< \frac{3}{4}\)
Chứng minh rằng: \(\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+\frac{4}{3^4}+....................+\frac{100}{3^{100}}< \frac{3}{4}\)
Cho biểu thức \(C=\dfrac{1}{3}-\dfrac{2}{3^2}+\dfrac{3}{3^3}-\dfrac{4}{3^4}+...+\dfrac{99}{3^{99}}-\dfrac{100}{3^{100}}\)
Chứng minh \(C< \dfrac{3}{16}\)
CMR: \(C=\dfrac{1}{3}+\dfrac{2}{3^2}+\dfrac{3}{3^3}+...+\dfrac{99}{3^{99}}+\dfrac{100}{3^{100}}< \dfrac{3}{4}\)
