D=5/4+5/4^2+5/4^3+....+5/4^99
4D=4(5/4+5/4^2+5/4^3+....+5/4^99)
4D=5+5/4+5/4^2+5/4^3+....+5/4^98
Lấy 4D-D=(5+5/4+5/4^2+5/4^3+....+5/4^98)-(5/4+5/4^2+5/4^3+....+5/4^99)
=>3D=5-5/4^99
D=5/3-5/3x4^99<5/3
=>d<5/3(ĐPCM)
`Answer:`
\(D=\frac{5}{4}+\frac{5}{4^2}+\frac{5}{4^3}+\frac{5}{4^4}+...+\frac{5}{4^{99}}\)
\(\Rightarrow4D=5+\frac{5}{4}+\frac{5}{4^2}+\frac{5}{4^3}+...+\frac{5}{4^{98}}\)
\(\Rightarrow4D-D=\left(5+\frac{5}{4}+\frac{5}{4^2}+\frac{5}{4^3}+...+\frac{5}{4^{98}}\right)-\left(5+\frac{5}{4^2}+\frac{5}{4^3}+\frac{5}{4^4}+...+\frac{5}{4^{99}}\right)\)
\(\Rightarrow3D=5-\frac{5}{4^{99}}\)
\(\Rightarrow D=\left(5-\frac{5}{4^{99}}\right):3\)
\(\Rightarrow D=\frac{5}{3}-\frac{5}{4^{99}.3}< \frac{5}{3}\)
Vậy `D<5/3`
