Question

[Pinz]

Cho C = \(\frac{5}{4}\) + \(\frac{5}{4^2}\) + \(\frac{5}{4^3}\) +  ...  + \(\frac{5}{4^{99}}\)

Chứng minh rằng C < \(\frac{5}{3}\)

Answer 1

[kudo shinichi]

\(C=\frac{5}{4}+\frac{5}{4^2}+\frac{5}{4^3}+...+\frac{5}{4^{99}}\)

\(4C=5+\frac{5}{4}+\frac{5}{4^2}+\frac{5}{4^3}+...+\frac{5}{4^{98}}\)

\(4C-C=\left(5+\frac{5}{4}+...+\frac{5}{4^{98}}\right)-\left(\frac{5}{4}+\frac{5}{4^2}+...+\frac{5}{4^{99}}\right)\)

\(3C=5-\frac{5}{4^{99}}\)

\(C=\frac{5-\frac{5}{4^{99}}}{3}\)

\(C=\frac{5}{3}-\frac{5}{4^{99}.3}< C\)

                                đpcm

Answer 2

[Nguyễn Tũn]

dễ ẹc!!!!!!!!